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    "Chapter 2\n",
    "======\n",
    "______\n",
    "\n",
    "This chapter introduces more PyMC syntax and design patterns, and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model."
   ]
  },
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   "source": [
    "## A little more on PyMC\n",
    "\n",
    "### Parent and Child relationships\n",
    "\n",
    "To assist with describing Bayesian relationships, and to be consistent with PyMC's documentation, we introduce *parent and child* variables. \n",
    "\n",
    "*  *parent variables* are variables that influence another variable. \n",
    "\n",
    "*  *child variable* are variables that are affected by other variables, i.e. are the subject of parent variables. \n",
    "\n",
    "A variable can be both a parent and child. For example, consider the PyMC code below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "source": [
    "import pymc as pm\n",
    "\n",
    "\n",
    "parameter = pm.Exponential(\"poisson_param\", 1)\n",
    "data_generator = pm.Poisson(\"data_generator\", parameter)\n",
    "data_plus_one = data_generator + 1"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`parameter` controls the parameter of `data_generator`, hence influences its values. The former is a parent of the latter. By symmetry, `data_generator` is a child of `parameter`.\n",
    "\n",
    "Likewise, `data_generator` is a parent to the variable `data_plus_one` (hence making `data_generator` both a parent and child variable). Although it does not look like one, `data_plus_one` should be treated as a PyMC variable as it is a *function* of another PyMC variable, hence is a child variable to `data_generator`.\n",
    "\n",
    "This nomenclature is introduced to help us describe relationships in PyMC modeling. You can access a variable's children and parent variables using the `children` and `parents` attributes attached to variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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    {
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     "text": [
      "Children of `parameter`: \n",
      "{<pymc.distributions.new_dist_class.<locals>.new_class 'data_generator' at 0x7f812404a8d0>}\n",
      "\n",
      "Parents of `data_generator`: \n",
      "{'mu': <pymc.distributions.new_dist_class.<locals>.new_class 'poisson_param' at 0x7f812404a898>}\n",
      "\n",
      "Children of `data_generator`: \n",
      "{<pymc.PyMCObjects.Deterministic '(data_generator_add_1)' at 0x7f812404a908>}\n"
     ]
    }
   ],
   "source": [
    "print(\"Children of `parameter`: \")\n",
    "print(parameter.children)\n",
    "print(\"\\nParents of `data_generator`: \")\n",
    "print(data_generator.parents)\n",
    "print(\"\\nChildren of `data_generator`: \")\n",
    "print(data_generator.children)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of course a child can  have more than one parent, and a parent can have many children."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### PyMC Variables\n",
    "\n",
    "All PyMC variables also expose a `value` attribute. This method produces the *current* (possibly random) internal value of the variable. If the variable is a child variable, its value changes given the variable's parents' values. Using the same variables from before:"
   ]
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   "execution_count": 3,
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     "text": [
      "parameter.value = 0.032177775515776275\n",
      "data_generator.value = 0\n",
      "data_plus_one.value = 1\n"
     ]
    }
   ],
   "source": [
    "print(\"parameter.value =\", parameter.value)\n",
    "print(\"data_generator.value =\", data_generator.value)\n",
    "print(\"data_plus_one.value =\", data_plus_one.value)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyMC is concerned with two types of programming variables: `stochastic` and `deterministic`.\n",
    "\n",
    "*  *stochastic variables* are variables that are not deterministic, i.e., even if you knew all the values of the variables' parents (if it even has any parents), it would still be random. Included in this category are instances of classes `Poisson`, `DiscreteUniform`, and `Exponential`.\n",
    "\n",
    "*  *deterministic variables* are variables that are not random if the variables' parents were known. This might be confusing at first: a quick mental check is *if I knew all of variable `foo`'s parent variables, I could determine what `foo`'s value is.* \n",
    "\n",
    "We will detail each below.\n",
    "\n",
    "#### Initializing Stochastic variables\n",
    "\n",
    "Initializing a stochastic variable requires a `name` argument, plus additional parameters that are class specific. For example:\n",
    "\n",
    "`some_variable = pm.DiscreteUniform(\"discrete_uni_var\", 0, 4)`\n",
    "\n",
    "where 0, 4 are the `DiscreteUniform`-specific lower and upper bound on the random variable. The [PyMC docs](http://pymc-devs.github.com/pymc/distributions.html) contain the specific parameters for stochastic variables. (Or use `object??`, for example `pm.DiscreteUniform??` if you are using IPython!)\n",
    "\n",
    "The `name` attribute is used to retrieve the posterior distribution later in the analysis, so it is best to use a descriptive name. Typically, I use the Python variable's name as the `name`.\n",
    "\n",
    "For multivariable problems, rather than creating a Python array of stochastic variables, addressing the `size` keyword in the call to a `Stochastic` variable creates multivariate array of (independent) stochastic variables. The array behaves like a Numpy array when used like one, and references to its `value` attribute return Numpy arrays.  \n",
    "\n",
    "The `size` argument also solves the annoying case where you may have many variables $\\beta_i, \\; i = 1,...,N$ you wish to model. Instead of creating arbitrary names and variables for each one, like:\n",
    "\n",
    "    beta_1 = pm.Uniform(\"beta_1\", 0, 1)\n",
    "    beta_2 = pm.Uniform(\"beta_2\", 0, 1)\n",
    "    ...\n",
    "\n",
    "we can instead wrap them into a single variable:\n",
    "\n",
    "    betas = pm.Uniform(\"betas\", 0, 1, size=N)\n",
    "\n",
    "#### Calling `random()`\n",
    "We can also call on a stochastic variable's `random()` method, which (given the parent values) will generate a new, random value. Below we demonstrate this using the texting example from the previous chapter."
   ]
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     "text": [
      "lambda_1.value = 4.970\n",
      "lambda_2.value = 1.039\n",
      "tau.value = 5.000 \n",
      "\n",
      "After calling random() on the variables...\n",
      "lambda_1.value = 1.411\n",
      "lambda_2.value = 1.806\n",
      "tau.value = 3.000\n"
     ]
    }
   ],
   "source": [
    "lambda_1 = pm.Exponential(\"lambda_1\", 1)  # prior on first behaviour\n",
    "lambda_2 = pm.Exponential(\"lambda_2\", 1)  # prior on second behaviour\n",
    "tau = pm.DiscreteUniform(\"tau\", lower=0, upper=10)  # prior on behaviour change\n",
    "\n",
    "print(\"lambda_1.value = %.3f\" % lambda_1.value)\n",
    "print(\"lambda_2.value = %.3f\" % lambda_2.value)\n",
    "print(\"tau.value = %.3f\" % tau.value, \"\\n\")\n",
    "\n",
    "lambda_1.random(), lambda_2.random(), tau.random()\n",
    "\n",
    "print(\"After calling random() on the variables...\")\n",
    "print(\"lambda_1.value = %.3f\" % lambda_1.value)\n",
    "print(\"lambda_2.value = %.3f\" % lambda_2.value)\n",
    "print(\"tau.value = %.3f\" % tau.value)"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The call to `random` stores a new value into the variable's `value` attribute. In fact, this new value is stored in the computer's cache for faster recall and efficiency."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **Warning**: *Don't update stochastic variables' values in-place.*\n",
    "\n",
    "\n",
    "Straight from the PyMC docs, we quote [4]:\n",
    "\n",
    "> `Stochastic` objects' values should not be updated in-place. This confuses PyMC's caching scheme... The only way a stochastic variable's value should be updated is using statements of the following form:\n",
    "\n",
    "        A.value = new_value\n",
    "\n",
    "> The following are in-place updates and should **never** be used:\n",
    "\n",
    "    \n",
    "        A.value += 3\n",
    "        A.value[2,1] = 5\n",
    "        A.value.attribute = new_attribute_value\n",
    "    "
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Deterministic variables\n",
    "\n",
    "Since most variables you will be modeling are stochastic, we distinguish deterministic variables with a `pymc.deterministic` wrapper. (If you are unfamiliar with Python wrappers (also called decorators), that's no problem. Just prepend the `pymc.deterministic` decorator before the variable declaration and you're good to go. No need to know more. ) The declaration of a deterministic variable uses a Python function:\n",
    "\n",
    "    @pm.deterministic\n",
    "    def some_deterministic_var(v1=v1,):\n",
    "         #jelly goes here.\n",
    "\n",
    "For all purposes, we can treat the object `some_deterministic_var` as a variable and not a Python function. \n",
    "\n",
    "Prepending with the wrapper is the easiest way, but not the only way, to create deterministic variables: elementary operations, like addition, exponentials etc. implicitly create deterministic variables. For example, the following returns a deterministic variable:"
   ]
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   "cell_type": "code",
   "execution_count": 5,
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    {
     "data": {
      "text/plain": [
       "pymc.PyMCObjects.Deterministic"
      ]
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     "output_type": "execute_result"
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   "source": [
    "type(lambda_1 + lambda_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The use of the `deterministic` wrapper was seen in the previous chapter's text-message example.  Recall the model for $\\lambda$ looked like: \n",
    "\n",
    "$$\n",
    "\\lambda = \n",
    "\\begin{cases}\n",
    "\\lambda_1  & \\text{if } t \\lt \\tau \\cr\n",
    "\\lambda_2 & \\text{if } t \\ge \\tau\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "And in PyMC code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
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   "source": [
    "import numpy as np\n",
    "n_data_points = 5  # in CH1 we had ~70 data points\n",
    "\n",
    "\n",
    "@pm.deterministic\n",
    "def lambda_(tau=tau, lambda_1=lambda_1, lambda_2=lambda_2):\n",
    "    out = np.zeros(n_data_points)\n",
    "    out[:tau] = lambda_1  # lambda before tau is lambda1\n",
    "    out[tau:] = lambda_2  # lambda after tau is lambda2\n",
    "    return out"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. \n",
    "\n",
    "Inside the deterministic decorator, the `Stochastic` variables passed in behave like scalars or Numpy arrays (if multivariable), and *not* like `Stochastic` variables. For example, running the following:\n",
    "\n",
    "    @pm.deterministic\n",
    "    def some_deterministic(stoch=some_stochastic_var):\n",
    "        return stoch.value**2\n",
    "\n",
    "\n",
    "will return an `AttributeError` detailing that `stoch` does not have a `value` attribute. It simply needs to be `stoch**2`. During the learning phase, it's the variable's `value` that is repeatedly passed in, not the actual variable.  \n",
    "\n",
    "Notice in the creation of the deterministic function we added defaults to each variable used in the function. This is a necessary step, and all variables *must* have default values. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Including observations in the Model\n",
    "\n",
    "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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    {
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Jb3T39WY2sf9TT8/mnfsSj20eVqfmYWXjAgAAAPqUZDV5uqSn3X2NJJnZ3ZIulbSiZMyV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\npka8vwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80df785780>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from IPython.core.pylabtools import figsize\n",
    "from matplotlib import pyplot as plt\n",
    "figsize(12.5, 4)\n",
    "\n",
    "\n",
    "samples = [lambda_1.random() for i in range(20000)]\n",
    "plt.hist(samples, bins=70, normed=True, histtype=\"stepfilled\")\n",
    "plt.title(\"Prior distribution for $\\lambda_1$\")\n",
    "plt.xlim(0, 8);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n",
    "\n",
    "PyMC stochastic variables have a keyword argument `observed` which accepts a boolean (`False` by default). The keyword `observed` has a very simple role: fix the variable's current value, i.e. make `value` immutable. We have to specify an initial `value` in the variable's creation, equal to the observations we wish to include, typically an array (and it should be an Numpy array for speed). For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "value:  [10  5]\n",
      "calling .random()\n",
      "value:  [10  5]\n"
     ]
    }
   ],
   "source": [
    "data = np.array([10, 5])\n",
    "fixed_variable = pm.Poisson(\"fxd\", 1, value=data, observed=True)\n",
    "print(\"value: \", fixed_variable.value)\n",
    "print(\"calling .random()\")\n",
    "fixed_variable.random()\n",
    "print(\"value: \", fixed_variable.value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is how we include data into our models: initializing a stochastic variable to have a *fixed value*. \n",
    "\n",
    "To complete our text message example, we fix the PyMC variable `observations` to the observed dataset. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10 25 15 20 35]\n"
     ]
    }
   ],
   "source": [
    "# We're using some fake data here\n",
    "data = np.array([10, 25, 15, 20, 35])\n",
    "obs = pm.Poisson(\"obs\", lambda_, value=data, observed=True)\n",
    "print(obs.value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Finally...\n",
    "\n",
    "We wrap all the created variables into a `pm.Model` class. With this `Model` class, we can analyze the variables as a single unit. This is an optional step, as the fitting algorithms can be sent an array of the variables rather than a `Model` class. I may or may not use this class in future examples ;)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model = pm.Model([obs, lambda_, lambda_1, lambda_2, tau])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modeling approaches\n",
    "\n",
    "A good starting point in Bayesian modeling is to think about *how your data might have been generated*. Put yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n",
    "\n",
    "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n",
    "\n",
    "1.  We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n",
    "\n",
    "2.  Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n",
    "\n",
    "3.  Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the later behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n",
    "\n",
    "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n",
    "\n",
    "5.  Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n",
    "\n",
    "    What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n",
    "\n",
    "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n",
    "\n",
    "\n",
    "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n",
    "\n",
    "<img src=\"http://i.imgur.com/7J30oCG.png\" width = 700/>\n",
    "\n",
    "\n",
    "PyMC, and other probabilistic programming languages, have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [5]:\n",
    "\n",
    "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Same story; different ending.\n",
    "\n",
    "Interestingly, we can create *new datasets* by retelling the story.\n",
    "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n",
    "\n",
    "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "21\n"
     ]
    }
   ],
   "source": [
    "tau = pm.rdiscrete_uniform(0, 80)\n",
    "print(tau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from an $\\text{Exp}(\\alpha)$ distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.7789591495 62.1938883352\n"
     ]
    }
   ],
   "source": [
    "alpha = 1. / 20.\n",
    "lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n",
    "print(lambda_1, lambda_2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3\\.  For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from  $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4\\. Plot the artificial dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Pnz6dz3zmM3zyk58EYMiQIZSWljYsP++88xg2bBi9evXi9NNPb3J85513Hn369GHnnXfm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d7c1ada0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(np.arange(80), data, color=\"#348ABD\")\n",
    "plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n",
    "plt.xlabel(\"Time (days)\")\n",
    "plt.ylabel(\"count of text-msgs received\")\n",
    "plt.title(\"Artificial dataset\")\n",
    "plt.xlim(0, 80)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. PyMC's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability.  \n",
    "\n",
    "\n",
    "The ability to generate artificial datasets is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TO4HZkg6WtAvwQeC6cqplZmZmZtZ/Ople/iVJnwWWkjXivxMR95dWMzMzMzOz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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d79baeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_artificial_sms_dataset():\n",
    "    tau = pm.rdiscrete_uniform(0, 80)\n",
    "    alpha = 1. / 20.\n",
    "    lambda_1, lambda_2 = pm.rexponential(alpha, 2)\n",
    "    data = np.r_[pm.rpoisson(lambda_1, tau), pm.rpoisson(lambda_2, 80 - tau)]\n",
    "    plt.bar(np.arange(80), data, color=\"#348ABD\")\n",
    "    plt.bar(tau - 1, data[tau - 1], color=\"r\", label=\"user behaviour changed\")\n",
    "    plt.xlim(0, 80)\n",
    "\n",
    "figsize(12.5, 5)\n",
    "plt.suptitle(\"More examples of artificial datasets\", fontsize=14)\n",
    "for i in range(1, 5):\n",
    "    plt.subplot(4, 1, i)\n",
    "    plot_artificial_sms_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Later we will see how we use this to make predictions and test the appropriateness of our models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Example: Bayesian A/B testing\n",
    "\n",
    "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n",
    "\n",
    "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n",
    "\n",
    "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n",
    "\n",
    "### A Simple Case\n",
    "\n",
    "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n",
    "\n",
    "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n",
    "\n",
    "- fraction of users who make purchases, \n",
    "- frequency of social attributes, \n",
    "- percent of internet users with cats etc. \n",
    "\n",
    "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n",
    "\n",
    "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n",
    "\n",
    "\n",
    "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n",
    "\n",
    "To set up a Bayesian model, we need to assign prior distributions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "# The parameters are the bounds of the Uniform.\n",
    "p = pm.Uniform('p', lower=0, upper=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Had we had stronger beliefs, we could have expressed them in the prior above.\n",
    "\n",
    "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if  $X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[False False False ..., False False False]\n",
      "77\n"
     ]
    }
   ],
   "source": [
    "# set constants\n",
    "p_true = 0.05  # remember, this is unknown.\n",
    "N = 1500\n",
    "\n",
    "# sample N Bernoulli random variables from Ber(0.05).\n",
    "# each random variable has a 0.05 chance of being a 1.\n",
    "# this is the data-generation step\n",
    "occurrences = pm.rbernoulli(p_true, N)\n",
    "\n",
    "print(occurrences)  # Remember: Python treats True == 1, and False == 0\n",
    "print(occurrences.sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The observed frequency is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "What is the observed frequency in Group A? 0.0513\n",
      "Does this equal the true frequency? False\n"
     ]
    }
   ],
   "source": [
    "# Occurrences.mean is equal to n/N.\n",
    "print(\"What is the observed frequency in Group A? %.4f\" % occurrences.mean())\n",
    "print(\"Does this equal the true frequency? %s\" % (occurrences.mean() == p_true))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We combine the observations into the PyMC `observed` variable, and run our inference algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 18000 of 18000 complete in 1.5 sec"
     ]
    }
   ],
   "source": [
    "# include the observations, which are Bernoulli\n",
    "obs = pm.Bernoulli(\"obs\", p, value=occurrences, observed=True)\n",
    "\n",
    "# To be explained in chapter 3\n",
    "mcmc = pm.MCMC([p, obs])\n",
    "mcmc.sample(18000, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the posterior distribution of the unknown $p_A$ below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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NPbtGQwZWxVI/AOBwsQ/GyRlHWOTpIYr+mjO+58BBbWrfG0vdQwdVZuYifQui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\noEQYjAMAAAAlwmAcAAAAKJH/DzuwK5wEwruJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d785e470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 4)\n",
    "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n",
    "plt.vlines(p_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
    "plt.hist(mcmc.trace(\"p\")[:], bins=25, histtype=\"stepfilled\", normed=True)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n",
    "\n",
    "### *A* and *B* Together\n",
    "\n",
    "A similar analysis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using PyMC's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (significantly less than $N_A$) and we will simulate site B's data like we did for site A's data )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Obs from Site A:  [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n",
      "Obs from Site B:  [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n"
     ]
    }
   ],
   "source": [
    "import pymc as pm\n",
    "figsize(12, 4)\n",
    "\n",
    "# these two quantities are unknown to us.\n",
    "true_p_A = 0.05\n",
    "true_p_B = 0.04\n",
    "\n",
    "# notice the unequal sample sizes -- no problem in Bayesian analysis.\n",
    "N_A = 1500\n",
    "N_B = 750\n",
    "\n",
    "# generate some observations\n",
    "observations_A = pm.rbernoulli(true_p_A, N_A)\n",
    "observations_B = pm.rbernoulli(true_p_B, N_B)\n",
    "print(\"Obs from Site A: \", observations_A[:30].astype(int), \"...\")\n",
    "print(\"Obs from Site B: \", observations_B[:30].astype(int), \"...\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.054\n",
      "0.0333333333333\n"
     ]
    }
   ],
   "source": [
    "print(observations_A.mean())\n",
    "print(observations_B.mean())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 20000 of 20000 complete in 2.6 sec"
     ]
    }
   ],
   "source": [
    "# Set up the pymc model. Again assume Uniform priors for p_A and p_B.\n",
    "p_A = pm.Uniform(\"p_A\", 0, 1)\n",
    "p_B = pm.Uniform(\"p_B\", 0, 1)\n",
    "\n",
    "\n",
    "# Define the deterministic delta function. This is our unknown of interest.\n",
    "@pm.deterministic\n",
    "def delta(p_A=p_A, p_B=p_B):\n",
    "    return p_A - p_B\n",
    "\n",
    "# Set of observations, in this case we have two observation datasets.\n",
    "obs_A = pm.Bernoulli(\"obs_A\", p_A, value=observations_A, observed=True)\n",
    "obs_B = pm.Bernoulli(\"obs_B\", p_B, value=observations_B, observed=True)\n",
    "\n",
    "# To be explained in chapter 3.\n",
    "mcmc = pm.MCMC([p_A, p_B, delta, obs_A, obs_B])\n",
    "mcmc.sample(20000, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we plot the posterior distributions for the three unknowns: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p_A_samples = mcmc.trace(\"p_A\")[:]\n",
    "p_B_samples = mcmc.trace(\"p_B\")[:]\n",
    "delta_samples = mcmc.trace(\"delta\")[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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//OUv9OzZk6VLl/LP//zPVY+dcsopLFq0iNzcXDIyMujTpw/Tp0/n4MGDJ+3n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d7897080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 10)\n",
    "\n",
    "# histogram of posteriors\n",
    "\n",
    "ax = plt.subplot(311)\n",
    "\n",
    "plt.xlim(0, .1)\n",
    "plt.hist(p_A_samples, histtype='stepfilled', bins=25, alpha=0.85,\n",
    "         label=\"posterior of $p_A$\", color=\"#A60628\", normed=True)\n",
    "plt.vlines(true_p_A, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n",
    "\n",
    "ax = plt.subplot(312)\n",
    "\n",
    "plt.xlim(0, .1)\n",
    "plt.hist(p_B_samples, histtype='stepfilled', bins=25, alpha=0.85,\n",
    "         label=\"posterior of $p_B$\", color=\"#467821\", normed=True)\n",
    "plt.vlines(true_p_B, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "\n",
    "ax = plt.subplot(313)\n",
    "plt.hist(delta_samples, histtype='stepfilled', bins=30, alpha=0.85,\n",
    "         label=\"posterior of delta\", color=\"#7A68A6\", normed=True)\n",
    "plt.vlines(true_p_A - true_p_B, 0, 60, linestyle=\"--\",\n",
    "           label=\"true delta (unknown)\")\n",
    "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n",
    "plt.legend(loc=\"upper right\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$.  \n",
    "\n",
    "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability site A is WORSE than site B: 0.017\n",
      "Probability site A is BETTER than site B: 0.983\n"
     ]
    }
   ],
   "source": [
    "# Count the number of samples less than 0, i.e. the area under the curve\n",
    "# before 0, represent the probability that site A is worse than site B.\n",
    "print(\"Probability site A is WORSE than site B: %.3f\" % \\\n",
    "    (delta_samples < 0).mean())\n",
    "\n",
    "print(\"Probability site A is BETTER than site B: %.3f\" % \\\n",
    "    (delta_samples > 0).mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n",
    "\n",
    "Try playing with the parameters `true_p_A`, `true_p_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n",
    "\n",
    "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An algorithm for human deceit\n",
    "\n",
    "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n",
    "\n",
    "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n",
    "\n",
    "### The Binomial Distribution\n",
    "\n",
    "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n",
    "\n",
    "$$P( X = k ) =  {{N}\\choose{k}}  p^k(1-p)^{N-k}$$\n",
    "\n",
    "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$), and $p$ is the probability of a single event. The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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TMXR8fA99l+hL/c/iY/6BZnaKReWGBwKY2V1m9tF4vUcRXSmrCUr6RPKiJF+kYzudCfJo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\npMwoyRcRERERKTNK8kVEREREysz/Bz7ixUPJmoxIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d704b898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 4)\n",
    "\n",
    "import scipy.stats as stats\n",
    "binomial = stats.binom\n",
    "\n",
    "parameters = [(10, .4), (10, .9)]\n",
    "colors = [\"#348ABD\", \"#A60628\"]\n",
    "\n",
    "for i in range(2):\n",
    "    N, p = parameters[i]\n",
    "    _x = np.arange(N + 1)\n",
    "    plt.bar(_x - 0.5, binomial.pmf(_x, N, p), color=colors[i],\n",
    "            edgecolor=colors[i],\n",
    "            alpha=0.6,\n",
    "            label=\"$N$: %d, $p$: %.1f\" % (N, p),\n",
    "            linewidth=3)\n",
    "\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlim(0, 10.5)\n",
    "plt.xlabel(\"$k$\")\n",
    "plt.ylabel(\"$P(X = k)$\")\n",
    "plt.title(\"Probability mass distributions of binomial random variables\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n",
    "\n",
    "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Example: Cheating among students\n",
    "\n",
    "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n",
    "\n",
    "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n",
    "\n",
    "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n",
    "\n",
    "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use PyMC to dig through this noisy model, and find a posterior distribution for the true frequency of liars. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in PyMC. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "N = 100\n",
    "p = pm.Uniform(\"freq_cheating\", 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "true_answers = pm.Bernoulli(\"truths\", p, size=N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ True False  True  True  True False False  True False  True  True False\n",
      "  True  True False  True False  True  True False  True False  True  True\n",
      "  True  True False  True  True False  True False  True False  True False\n",
      " False  True  True False  True  True False False  True False False False\n",
      "  True False  True  True False False False  True  True False False False\n",
      "  True  True  True False False False False False  True False False  True\n",
      "  True False False  True False False False False  True False  True False\n",
      " False False  True  True False False  True False  True  True  True False\n",
      " False False False  True]\n"
     ]
    }
   ],
   "source": [
    "first_coin_flips = pm.Bernoulli(\"first_flips\", 0.5, size=N)\n",
    "print(first_coin_flips.value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "second_coin_flips = pm.Bernoulli(\"second_flips\", 0.5, size=N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. We do this using a PyMC `deterministic` variable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "@pm.deterministic\n",
    "def observed_proportion(t_a=true_answers,\n",
    "                        fc=first_coin_flips,\n",
    "                        sc=second_coin_flips):\n",
    "\n",
    "    observed = fc * t_a + (1 - fc) * sc\n",
    "    return observed.sum() / float(N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, produces a proportion. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.58999999999999997"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observed_proportion.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expect to see approximately 3/4 of all responses be \"Yes\". \n",
    "\n",
    "The researchers observe a Binomial random variable, with `N = 100` and `p = observed_proportion` with `value = 35`:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X = 35\n",
    "\n",
    "observations = pm.Binomial(\"obs\", N, observed_proportion, observed=True,\n",
    "                           value=X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 40000 of 40000 complete in 10.4 sec"
     ]
    }
   ],
   "source": [
    "model = pm.Model([p, true_answers, first_coin_flips,\n",
    "                  second_coin_flips, observed_proportion, observations])\n",
    "\n",
    "# To be explained in Chapter 3!\n",
    "mcmc = pm.MCMC(model)\n",
    "mcmc.sample(40000, 15000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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/+Yl2npl2trYnvT+iRx8lfJEVBEFeEAVWtJFTVqzblekSAAAAvNCjjcglu5qN4YkVJ/gi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\nTLQBAACAEDDRBgAAAELw/wG/9pFRN8P3PwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d6d7c9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 3)\n",
    "p_trace = mcmc.trace(\"freq_cheating\")[:]\n",
    "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n",
    "         label=\"posterior distribution\", color=\"#348ABD\")\n",
    "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.3)\n",
    "plt.xlim(0, 1)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.05 to 0.35 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n",
    "\n",
    "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with a uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n",
    "\n",
    "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Alternative PyMC Model\n",
    "\n",
    "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n",
    "\n",
    "\\begin{align}\n",
    "P(\\text{\"Yes\"}) &=  P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\\\\\n",
    "& = \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\\\\\n",
    "& = \\frac{p}{2} + \\frac{1}{4}\n",
    "\\end{align}\n",
    "\n",
    "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In PyMC, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = pm.Uniform(\"freq_cheating\", 0, 1)\n",
    "\n",
    "\n",
    "@pm.deterministic\n",
    "def p_skewed(p=p):\n",
    "    return 0.5 * p + 0.25"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I could have typed `p_skewed  = 0.5*p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a `deterministic` variable, but I wanted to make the deterministic boilerplate explicit for clarity's sake. \n",
    "\n",
    "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n",
    "\n",
    "This is where we include our observed 35 \"Yes\" responses. In the declaration of the `pm.Binomial`, we include `value = 35` and `observed = True`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "yes_responses = pm.Binomial(\"number_cheaters\", 100, p_skewed,\n",
    "                            value=35, observed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we add all the variables of interest to a `Model` container and run our black-box algorithm over the model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 25000 of 25000 complete in 1.2 sec"
     ]
    }
   ],
   "source": [
    "model = pm.Model([yes_responses, p_skewed, p])\n",
    "\n",
    "# To Be Explained in Chapter 3!\n",
    "mcmc = pm.MCMC(model)\n",
    "mcmc.sample(25000, 2500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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y2ogdGW2EIEcJX/QKQtAviAM72gAAAEAEyGgjdmS0EYIcJXzRKwhBvyAO7GgDAAAAESCj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\niAALbQAAACAC/x+J2u8PdjKOOAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d6d9c5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 3)\n",
    "p_trace = mcmc.trace(\"freq_cheating\")[:]\n",
    "plt.hist(p_trace, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30,\n",
    "         label=\"posterior distribution\", color=\"#348ABD\")\n",
    "plt.vlines([.05, .35], [0, 0], [5, 5], alpha=0.2)\n",
    "plt.xlim(0, 1)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### More PyMC Tricks\n",
    "\n",
    "#### Protip: *Lighter* deterministic variables with `Lambda` class\n",
    "\n",
    "Sometimes writing a deterministic function using the `@pm.deterministic` decorator can seem like a chore, especially for a small function. I have already mentioned that elementary math operations *can* produce deterministic variables implicitly, but what about operations like indexing or slicing? Built-in `Lambda` functions can handle this with the elegance and simplicity required. For example,  \n",
    "\n",
    "    beta = pm.Normal(\"coefficients\", 0, size=(N, 1))\n",
    "    x = np.random.randn((N, 1))\n",
    "    linear_combination = pm.Lambda(lambda x=x, beta=beta: np.dot(x.T, beta))\n",
    "\n",
    "\n",
    "#### Protip: Arrays of PyMC variables\n",
    "There is no reason why we cannot store multiple heterogeneous PyMC variables in a Numpy array. Just remember to set the `dtype` of the array to `object` upon initialization. For example:\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "N = 10\n",
    "x = np.empty(N, dtype=object)\n",
    "for i in range(0, N):\n",
    "    x[i] = pm.Exponential('x_%i' % i, (i + 1) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The remainder of this chapter examines some practical examples of PyMC and PyMC modeling:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "##### Example: Challenger Space Shuttle Disaster <span id=\"challenger\"/>\n",
    "\n",
    "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Temp (F), O-Ring failure?\n",
      "[[ 66.   0.]\n",
      " [ 70.   1.]\n",
      " [ 69.   0.]\n",
      " [ 68.   0.]\n",
      " [ 67.   0.]\n",
      " [ 72.   0.]\n",
      " [ 73.   0.]\n",
      " [ 70.   0.]\n",
      " [ 57.   1.]\n",
      " [ 63.   1.]\n",
      " [ 70.   1.]\n",
      " [ 78.   0.]\n",
      " [ 67.   0.]\n",
      " [ 53.   1.]\n",
      " [ 67.   0.]\n",
      " [ 75.   0.]\n",
      " [ 70.   0.]\n",
      " [ 81.   0.]\n",
      " [ 76.   0.]\n",
      " [ 79.   0.]\n",
      " [ 75.   1.]\n",
      " [ 76.   0.]\n",
      " [ 58.   1.]]\n"
     ]
    },
    {
     "data": {
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LcCQwgtCbPgr4aNFFuoiIiIiIBLkvz+juj7j75939aHc/w90f7omA1KOeDvW2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\nBzNBWL/hM4KOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d77ea320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 3.5)\n",
    "np.set_printoptions(precision=3, suppress=True)\n",
    "challenger_data = np.genfromtxt(\"data/challenger_data.csv\", skip_header=1,\n",
    "                                usecols=[1, 2], missing_values=\"NA\",\n",
    "                                delimiter=\",\")\n",
    "# drop the NA values\n",
    "challenger_data = challenger_data[~np.isnan(challenger_data[:, 1])]\n",
    "\n",
    "# plot it, as a function of temperature (the first column)\n",
    "print(\"Temp (F), O-Ring failure?\")\n",
    "print(challenger_data)\n",
    "\n",
    "plt.scatter(challenger_data[:, 0], challenger_data[:, 1], s=75, color=\"k\",\n",
    "            alpha=0.5)\n",
    "plt.yticks([0, 1])\n",
    "plt.ylabel(\"Damage Incident?\")\n",
    "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n",
    "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n",
    "\n",
    "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n",
    "\n",
    "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n",
    "\n",
    "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6gVJqP65Tq/20rbby8vLYlV7gWWStaOoc+1tM+Ftd9wFWEwEW8/HTVjMB7nkCrWYCWt7b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\nIYQQQogJ6/8D7r1sBck0m/kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d77b9ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12, 3)\n",
    "\n",
    "\n",
    "def logistic(x, beta):\n",
    "    return 1.0 / (1.0 + np.exp(beta * x))\n",
    "\n",
    "x = np.linspace(-4, 4, 100)\n",
    "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\")\n",
    "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\")\n",
    "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\")\n",
    "plt.title(\"Logistic functon plotted for several value of $\\\\beta$ parameter\", fontsize=14)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n",
    "\n",
    "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n",
    "\n",
    "Some plots are below, with differing $\\alpha$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sZWth7Yn0AhgQYSI9JoT0WDMZMSFkxIYQH2rst9MOhRj1LezalIhgbVGWb3Mq\nObLFQkmdjQERQVw1LpGZQ2N6Uamit2jLEXY5HOgMgXvrEno9CbPPIGH2GZR/t4kD//wv1Vt2s+/+\nJzjy3BIy7ryB5Mt/gs7ov+dotdh59+WNTDkznfFTB/Xb+1Zfwel0sfKjPezYWADAaTMzmDZzKEKF\nRSj6CSpMogdxSc1JzqmwcKSykZyKRo5UWsivstBaR3J4kJ50t2M8NNZMZlwIKZHB/WbQXmewOVzk\nV1swm7SZQZrzfW41tVYHmXFmUqOUDfsKdQeOsPmaO8m851cMuPjcPtFzLKWk9Ku1HHz4hRPzFpvT\nUhjxwK0kzPbfVfxsVoeKD+4DHJ8LOj+nAoNBx5z5YxgxboCvZSkUXsEvwyT6mzPcFnani4JqK9nl\njRyuaCS7vIHs8kZqrC0XHgk26MiIDSEzTnOOM+PMDFIOcod8e7iSNUeqOFTeSGm9nSHRwQyNDeGS\n0QkMilLxb4FMxfdb2f/gM0iHg+F/+S2x0yf7WpJXkC4Xxz5aycF/vUTD4XwAEn96FlkP3UHwgJaD\nUBWK7mK12FnywgbKjtURGh7ERddOULNFKPoUfukMB3rMcE8ipaS8wU52eSOHyhs5WNbAwbIGSutb\nDtoLMeoYFmfGULibn55zFsMTzMSZ+2+IRUc02JwcrtDsempqBEmt9CSX1NnYt2UDM2b4b09cINHT\ncW9SSoo/XsX+h54leuo4sh66vU/MygBaGEjeq+9z8J8v4KxvQB9mpuaKmVzyt3v6RE+4P6DiMsHp\ncPH+4s3kHionJi6Uy248hfDIzncUKFt6F2VP76JihgMMIYR7mWkTU1N/HJFd1Wg/yTneX6o5yNuL\n6qg5XMnmlTkAxJgNjIgPZWRCKCMTQ8mMMxNkUD+coMV6j04KY3RSWJtpHl59hM0bDjO5JomsBDMj\nEkLJSggl1hw4g4L6E0IIki6YSdys0zj81GJfy/EqOoOBIb+4nMS5Z7L33oWUfLGG3BffYf22HEY/\neg/hWRm9rslud2JUcwj3GaSUfLlsF7mHyjGHmbjkukldcoQVir6CCpMIQCoa7OwvbWBfaT37SzUH\nud52coiFQSfIiA054RyPSgwlLtTkI8WBQa3V4bZrA3uL6zlY1sDrV45SfyoUPkNKSfFn37D33sew\nFpchDHrSfnMNQ++8AV1Q71zP5SV1LH11E1fffKqaYquPsHbFQb7/OhuDUc+Vv5xCUoqaEk/RN/HL\nMAnlDPf3TTKOAAAgAElEQVQMLik5Wm1lX2k9e4rr2VtST06FheY1mxRuYnRSGGMSQxmdFEZKZJAK\nrWgHKWWr9qmzOnhvZwmjk8LISghVC64oehx7TR0H//E8ea99AFISMXYE41/8G+bByT1ablV5A++8\n9AOnn5vJ6Ik9W5aid9i5uYAvlu5CCLjoZxPJGJHga0kKRY/hqTPcq11e27Zt683i+jxr1qwBQCcE\ng6KCOTczlt9NT+X5S7J4f8FYHp6bwYKJSUxOCcds1HGs1saKgxU8viafG9/byxVv7uLBFYf5YFcJ\nORWNbS613F84bs/jtPVHweGSSODtbcVc9dYubn5/H8+sK2BTQU0vqAwMmtuyt3HZ7Oz/2zM4aut9\nqsNbbNixjZEP38XUj54nJHUgNTv2se7c6zn26eoeK7Ohzsa7izZy6lnpfc4R9nX79BVHDpbx1Qe7\nAZh1wUivOML91ZY9hbKnb1Axw32UUJOeickRTEyOALS5kHMqGtl5rI5dxfXsOlZHZaODNUeqWXOk\nGoDIYANjB4QxbkAY4weEMyhK9Ry3RlSIkesnDwS0mUEOlTeys6iOIxWNTE6J8LE6BQBS4qht4Pu5\nNzJh0cOEDRvia0VeIfqUMUz76hV23fEPij/7hm033svgX1zG8D//Fp3Je/HtUkqWL93JiDFJjJua\n6rV8Fb6jpKiGj97aisslmTIjjfGqXhWKE6gwiX6KlJLCGis7jtWzo6iW7YV1lDVbbjo6xMD4geFM\nSg5nQnI48SrmuEusyq5kb0k9EwaGM3ZAmAqr6EUKlnzC/r89y6h//R9J55/tazleQ0pJ7kvvalPM\n2R1Ejs9i3AsPYU71zvywVeUNrPh4Dxf/bCJ6L6/0qOh9aqstvPnc99TVWBkxNomfXj5OLaih6Beo\nmGFFpzjuHG8vqtNehbVUNDpOSpMSGcTE5HAmJoczbkC4cuo8JL/KwtrcKrYerWNfaT2Do4KZMDCc\n84bFkhzZcpo3hXep3r6PrTfey4ALZjHsvpsR+r7Tbqu27GHbr/6EpeAYhshwxjxxH4lzZvhalsKP\nkC7JOy//QEFOJSlDorn0hlMwqEHBin6CihnuB3gztkgIQXJkMD8ZEccfzx7CkqtH89L8LH5zWgqn\npUZiNuooqLby0Z4yHvgqh/mv7+D3nxxgybZjHCxr6BPxxj0VqzUoKpgrxyXxyE+G8r9rxnDDKQNB\nQL295SIrfQV/inuLHDeCaV8swhgdDgE6T29b9oyaOJJpX71KwuzpOKpr2XrdPeQ8+xa92ckRiPhT\n++xptm3IoyCnEnOoiQuumeB1R7g/2bI3UPb0DSpmWNEqQghSo4NJjQ7molHxOFyS/aX1bDlay5aj\ntewtqWfXMe31yqYiokMMTEqJ4JSUcCYlRxARrJpWa5gMOsYPDGf8wLYXiHhjSxFDokOYmByOWfW+\newVTbBTpty7wtYwewRQdwYRXHyHnmTc58NCz7H/waSyFxYz46219qhdc0XmqKhr49osDAJxz4UjM\nKtRNoWgVFSah6BL1Nidbj9aysaCGjQU1lDVZKU8nYGRCKFNTI5maGsHgqGA1EM9DpJR8sLuUH/Jr\n2FtSz4h4M6cMimTqoAg1FZ6iQ4qWrWDHbX9D2uwk/vQsxj79F/QhKhSnPyJdkndf3kh+TgXDxyQx\n76rxvpakUPQ6Xo0ZFkLMAf6DFlbxspTykWbfRwBvAKmAHlgopXy1eT7KGe6bSCnJrbKwKV9zjHce\nq8fh+rFdJYaZODU1gqmpkYwdEIZJDcjxiEa7k62FtWzIqyG/ysLC8zOVM+xlXDa7V2dh8AfK125h\n6/X34KipI2rKWCa+9i9M0e3PclJT1cihPSVMnDa4l1Qqeppt6/NY8dEeQkJNXP+76ZjDVK+wov/h\ntZhhIYQOeBqYDYwCrhJCjGiW7BZgt5RyPHA2sFAI0eI5uYoZ9i7+ElskhGBIdAiXjk3kkZ9k8r9r\nx3D/rDTOy4whMthAcZ2ND/eUce/ybC5/Yyd//zqHVdmVLVbN8zX+Ys/jhBj1TBscxR1npPLYvGGt\nOsK1Vgd1VkcrR/sWf7NlW2xe8H/kLV7maxkd0hl7xp4+kakfPU/wwASqftjBhgtuoiGvqM30Lpfk\ns3d3YLf5XzvqKQKlfXaV6soGvlm+H4BzLhjZo45wX7dlb6Ps6Rs8CeycAhyUUuYCCCHeBi4E9jVJ\nI4HjQZDhQLmUslN31rq6Oqqrq1XPVyeIjY2lsLDQ1zJaIKVkQnwkZ6QNxumSHChrYH1eNRvyqjlc\nYeGbw1V8c7gKg04wfmAYp6VGctrgSLVcdBfYcrSWx7/LY3i8mdMGRzFtcCQJqgfIY0Y9fBcbr7gd\ne2U16bct6DP3n/AR6Zz66Ytsuvr31O3NZsP5v2LSm48SMWZ4i7QbVh9G6ASnzEj3gVKFt5FS8sX7\nu7HbnAwbncTwMUm+lqRQ+D0dhkkIIeYDs6WUv3JvXwtMkVLe1iRNGPARMAIIA66QUn7ePK+2wiTK\ny8sBiImJ6TM/Rv0ZKSUVFRWA5rA3pajWyve51aw7Us2u4jqaRFMwMiGU6WlRzEiLUg5dJ2i0O9ly\ntJZ1udofjgERQfxqajJjksJ8LS0gsBSXsenKO4idMZkRf7kVEaAzTrSGvaaOrdffQ8XaLRgiwjjl\nf08SOe7HB3tV5Q28+dz3LLj1dMIjg32oVOEttv+Qz1fLdhNiNnLd7dMJDVMx44r+i9dihj10hucD\n06SUdwohMoCvgLFSyrqmef3617+WVVVVpKZqK99ERkYyZswY0tPTGThwYCdPUeHv7Nmzh4qKCqZP\nnw78+Pjn+PYXX3/DnuJ6quJGsLmghrIDWwGIyBjP8HgzCVUHGJsUxoWzz271eLXdctvpkoRnjGNg\nRBCHtm/0uZ5A2bZX1fDKBT8nKDGOBW8/j9Dr/Upfd7annTKF7b95gFUff4ohzMx1Hy8mYlQma9as\nYe2Kg5x51gxOPSvDb/Sq7a5v19da2bfBhd3mZOBwK6kZsX6lT22r7Z7ePv45Ly8PgMmTJ3PnnXd6\nxRk+FXhASjnHvX0PIJsOohNCfAL8U0q51r29ErhbSrmpaV4LFy6UN9xwQ4syCgsLlTPcB+lMvTba\nnfyQX8N3OVVsyK/B6nCd+G5obAhnZURzZlo0ieE9G/t2/MLqq3ywq4SJyeEMjg7p0XIC0ZbOBguF\nS5eTcu2FfveEqrv2dNkdbPvFvZR8sQZjTBRT3n+akIzBfPXhbs65cBRGY/+agi0Q22dHSCl575VN\n5B4qJ3NUIhdcPb5X2nFftKUvUfb0Lp72DHsSM7wRGCqEGAwUAVcCVzVLkwucA6wVQiQCw4DDnZOs\n6M+EGPWcmR7NmenRWBwuNuXX8N2RKtbnVXOovJFD5Y289EMhIxNCOSsjmhlpUcSY+9YsAD2N3eni\nWJ2NP36eTViQnhnp0ZyVHkWKejwOgN4czKCfXeRrGT2Czmhg/AsPseX6P1L29fdsvOw2pnzwDHMv\nHetraQovsW97EbmHygkOMXLOBSP97g+dQuHPdGZqtSf4cWq1h4UQN6H1EL8ghBgAvAoMcB/yTynl\nkub5tBUzrHqG+ybeqFebw8XGghpWH65kfW41VqfWXgUwdkAYZ2dEc0ZaFOFBnvyvUwC4pGRPcT3f\nHK7iu5xKxiSFcd+sNF/LUvQCTouVLQv+QPm3GwlKimPKB88Smpbia1mKbuJ0uFj0n++ormhk9iWj\nGTNZ1alCAV6eZ9hbKGe4f+Htem20O1mfpznGm/JrsLtH3xl1gqmpEcwcGsOUQRFqHuNO4HRJyhvs\nasBiP8LZYGHTNXdS+f1WgpMTmfL+M5gHq/tvILN1fR4rP9pDTHwo1912Ojp1D1QoAC/OM+xN1DzD\niu4QYtRzdkY0fz03nXeuGc2dM1KZMDAch0uy5kg1D67I4co3d/GfNXnsKKrD1ck/ek0D8PsLep1o\n0xFelV3JtzmV2JyuVr9vj75iS0thCUffbTExTq/jTXvqzcFMeuPfRE0Zi+VoMRsvvZXGgmNeyz8Q\n6CvtE8Bmc7B+VTYA08/N7HVHuC/Z0h9Q9vQN6u+jD9m1axf333+/r2UEJGFBBmYPi+WRnwzlzatG\n8aspA8mIDaHO5uSzfeXc9elBfv7OHhZvLqKoxupruQGJUS/4eE8ZV7+1iyfX5rO3pJ7efJLkD0in\nk4OPvEDBkk98LcUr1NVYqK5sxBBqZvKbC4mcMJLG/CI2X30n9upaX8tTdIGt63Kpr7WSmBxB5qhE\nX8tRKAISFSbRSXbs2EFubi4AR44c4dZbb+1SPs888wwbNmwgIiKCp59+2psS/QZf1GtORSNfZ1ey\n8lAFZfX2E/vHJoVx3rAYzkiLIqSfjZzvLsW1NlYeqmDFIW3u6KcuHE6oqf/YsO5QLhvn30rW324n\n6YKZvpbTLT57dwcR0SFMPzcTAHtVDRsu/DV1+3OIPWMyk95c2OeWp+7LWBrtvPjvb7BaHFx2w2QG\nD43ztSSFwq/wyzCJQGfnzp3U1NQwb9485s2bx4oVK7qc1y233MLcuXO9qE4BkBYTwo2nDOSNK0fx\nyNyhzBoaTZBesONYHY9+m8cVb+7i39/ksqOort/1cnaVxHATV09I4uVLs/jTzLR+5QgDhA0dzKS3\nFrLn3oVUrNvqazldpii/itzscqbM+HGwpDEqgomvP4opPoby7zax++5/q+sigPjh28NYLQ5SM2KV\nI6xQdINeHYK/bds2WusZDhT27dvHZZddBmjnkpWVBWg9xIsXL0YIceKH5PhnIQSTJ09Wjm8voxOC\nCcnhTEgO57fTnHybU8VXB8rZVVzPVwcr+OpgBSmRQcwZFss5mTHEmI1qfscOEEKQHtv6/MRFtVZq\nrU4yY0MQQvQ5W0aMymTssw+w7ab7Of3rxQTFx/Rq+d21p5SS1Z/tY/q5mZiazbxiTh3AxNf+xQ/z\nb+Hokk8wp6WQcduC7kr2a/pC+6yrsbBlnfaU8ozzMn2moy/Y0p9Q9vQNATMf1eLNRbyxteUgj2sn\nJLFg0oAO07eVzlMKCgoYNGgQe/bs4a233uLw4cM89thjAAwZMoQ///nPXc5b0bOEmvTMHR7L3OGx\nHK228uXBcr48UEFBtZWXNhayaFMhp6ZGklxTz2kuiV6n5ufsLEerrTyxJp9Qk47Zw2Ix25y+luR1\n4macwuS3H8cUF+1rKZ3mwK5i7DYnoyYmt/p91MSRjHvmAbbeeC8H//E85tSBDLjonF5WqegM36/K\nxmF3kTkqkQGDonwtR6EIaFTMsIcsW7aMefPmoddrj4gXLVpEZWUld955Z5fzXLJkCWvXrlUxwz7A\n6ZJsKqjh8/3lrM+rxj1LG3FmI3OGxzJneKyabqyTuKRke1Edy/eX80N+DaemRrBg0gAGhAf5Wlq/\nRkrJ4qfWMWPOMNKGxbebNuf5Jex/4Cl0QSZOee8pok8Z00sqFZ2hqryBRY9/h5SS6343ndiEMF9L\nUij8Em+uQKcArFbrCUcY4MCBA6SnpwMnh0k0RYVJ+C96nWBqaiRTUyOpaLDz1cEKPt9fTmGNlTe2\nHuOtbceYMiiC87PimJQcoXqLPUAnBBMGhjNhYDg1FgdfHazAqOzmc4QQXLxgIuEerDQ45KYracgp\nIP+1D9jy87s57bMXMA9RCzj4G2tXHMTlkoyelKwcYYXCC6iYYQ9Zv349V1xxBQDl5eVs3LiR++67\nD+hemIQarOJ7YsxGrhiXyMCaA4RPH8+n+8pYe6Sa9Xk1rM+rISHMyE+GxzF7eCyxagloj9ixaT3z\n24h7axpXr/CM7sYRRkS1HuvdHCEEWX+/g8a8IspWrWfTNXdx6icvYIqO6HLZ/kggx2WWFNWwd3sR\ner1g2qyhvpYT0Lb0R5Q9fYOaTcIDdu7cyZw5c3j33Xf5+OOPeemll3jttdcIDw/vcp4vvvgib7zx\nBmvXruWRRx6htlbN8elrhBCMHxjOfTPTePOqUdx4ykAGhJsoqbPz6uYirl2yi7+vzFEzUXSTXcX1\n/PqD/Xyyt4xGe2DHFtdn51Gxvm8tJqQzGBj/wt8IHzmUhuw8dvzmAaSr8wuvKHqGNV8eBGD8qake\n/8lRKBTto2KGPWDp0qXMnz/f1zICDn+vV09wScmWo7V8tq+Mdbk/xhanRQczb2Q8s4ZGq3mLO4lL\nSrYereWTvWXsOFbHzIxozs+KY3B04P2wl6/dwvab7mfqh88RmpHqazlepbHgGOvOux57RTVD77qR\noXfd6GtJ/Z5jR6t545nvMZr0/PKuMzGrcQ0KRbuoeYa9iE6nzNRf0QnB5JQI/nxOOq9fOYprJiQR\nHWIgp9LCk2vzueqtXTyzroD8KouvpQYMOiGYlBLBX85N57mLRxAWZODuzw/xXU6Vr6V1mtjTJ5L5\nx5vY8vM/4Kir97UcrxKSksS4Zx8AITi0cBGlX6/3taR+z6bvjgAwbsog5QgrFF6kV728bdsC83Hi\nxRdf7GsJil6gozXh40NN/HzSAN64chR/PHswoxJDabC7+HBPKTe+t5d7lx/ih/xqXCqEokNbHich\nTLPp61eMYmpqYMalDrrmAqJPHc+uOx/usfAZT+3ZlM1rj1Bb3b0/aXFnTWXo//0CpGTHLQ/QkFfU\nrfz8ha7Y09fUVDWyf9cxhE4wcdpgX8s5QSDa0p9R9vQNqstToegkRr2OszNieHzeMJ67eDhzh8di\n0gs2FdTypy8O84v39vLh7lIa+uBcuz2FUa/DpG95O3K4JNnlDT5Q1Dmy/nYH9dl55L/6vq+lAFBZ\nXs/6VdkEBXd/jHTG7T8n/pxp2Ctr2PaL+3BarF5QqOgsW9blIl2S4aOTVKywQuFlVMywosfoT/Va\nY3Hw+f5yPtpTSmm9HQCzUcfs4bFcNDKeARFqrt2ukFdp4Z7lhxgQHsTFo+M5LTXSb6e5q88poHL9\nNlKuOt/XUvjyg12Yw4KYfq53ViazV9Ww7tzracwvIuXaCxj96D1eyVfhGVaLg/8+shqb1cG1t5xG\nUnKkryUpFAGBihlWKHqRiGADV4xLZPEVo/jTrCGMTtJCKD7YVcr1/9vDgysOs+uYmoWis6RGB7P4\nilHMy4rj3e3FXP+/Pby/q4R6P+x1D01L8QtHuK7GwoFdxUw8zXuP0o1REYx/+R/ogkwUvPERBUs+\n8Vreio7ZuakAm9VBSlq0coQVih5AxQwrFG68Eaul1wlmpEXz2PnDeOai4ZyTGYNOCNYcqeb3nxzk\nto8OsCq7AoerbzvF3ox7M+gEZ2VE8+SFw/nj2UPYW1LP1qP9ayrCzthz89pcRo4f6PUBVpFjhzPy\nn3cBsOePj1Kzc79X8+9NAiku0+V0sWXdEQAmT0/zrZhWCCRbBgLKnr5B9QwrFD1EZpyZP5w5mNev\nHMXV4xOJCNKzv7SBf67KZcE7u3l3RzF1VoevZQYUWQmh3DczjelpUb6W4pc4nS727yxi0vQhPZJ/\nytXnk3LNPFwWG1tvvA97df/6U+ILDuwupqbKQnScmYzh7S+nrVAouoaKGVb0GKpeT8bicLHiYAUf\n7Cohv1obhGQ26pg7PJaLRyeQoKZK6hb1NidbC2v9Kq7Y5XCgM/TuqvcOuxNDD8597bRY2XDBzdTs\n2E/ShbMY9/yDajXBHkJKyZvPredYQTXnXDiS8VP71lzWCkVPo2KGFQo/I9ig4/ysOF68NIuHZqcz\nfmAYDXYXS3eV8vN3dvPwqiMBMXOCv1LRYOed7cXc+N5ePtpTisXh21XTrKUVrD17Abayyl4ttycd\nYQB9cBDjnn8QvTmEYx+upPDdz3u0vP7M0SOVHCuoJsRsZNSEZF/LUSj6LCpmWKFw01uxWjohmDIo\nkn/9JJOnLxrO2RnRSODr7Ep+/cF+7vn8EJsKagJ6sJ0v4t4GRQXz5AXDuGtGKluO1vKzt3ezeHMR\n1RbfhKIExceQMHs6O257qNt16W9xhKHpg8j6x+8B2HPvY9TnFPhYUefwN3u2xaY1RwAYNzUVo8k/\nV7oMFFsGCsqevkH1DCsUPmRYnJk/nj2EVy8fycWj4wk26NhytJZ7l2dzy7L9rM6uxNnHB9t5EyEE\no5PCeODcdB47P5PyBrtPVwfMvPtX2CuqyFu01GcaeorkK35C0oWzcNY3sOPXf8FlV/Hv3qSyrJ5D\n+0rQ6wUTTlXhEQpFT6Jihn3E8uXLqa2tJScnh9jYWG688UZfS/I6/bFeu0ut1cEne8tYtruUykbN\nuRgQbuLSMQmcNyyWIIP6/xpo1GfnsX7eTUz94FnChvvfbADdwV5dy9qZC7AcLSb9tgUMu/dmX0vq\nM6z4cA/bNuQxelIyc+aP8bUchSIg8TRmWDnDnWTHjh3k5uYCcOTIEW699dZO51FTU8OIESPIycnB\nZDIxdOhQVq9ezaBBg7wt16cEUr36GzaHiy8PVvDezmIKa2wARAUbuGhUPPNGxhEe1LuDsvoa5Q12\n8qosjB8Q1iuDv/Lf/IiCNz/m1E9f6JHy1q/KZviYJKLjQr2ed0dUbtjOhotvASk55X9PEjt9Uq9r\n6Gs0Ntj47yOrcdhdXPe704lLDPe1JIUiIPHqADohxBwhxD4hxAEhxN1tpDlLCLFVCLFLCLGqtTSB\nHjO8c+dOampqmDdvHvPmzWPFihVdyiciIoKVK1cSFBSEEAKn0xnQ8aF9BX+K1TK5B9u9fOlI/jRz\nCJlxIVRZHLy6uYifvb2bl344SkWD3dcy28SfbNkaJXU2nlqbz20fHWDtkSpcPXz9pVw9j3HP/bXL\njnB79qyrsbDxuxyvzyvsKdFTx5Fxx3UgJTtufRBbRbVPdHQGf2+f2zfk47C7GDIszu8dYX+3ZaCh\n7OkbOuxeEkLogKeBWUAhsFEI8aGUcl+TNJHAM8B5UsqjQoi4nhLsS/bt28dll10GaI59VlYWoPUQ\nL168GCHECaf2+GchBJMnT2bu3Lkn5XX82O+//55p06aRmqpiwhQt0esEM9KjOSMtim2Fdby9vZit\nhbW8u6OED3aXMntYLJeNTWBAuFruuTNkJYTy4vws1uVW89a2Y7y6qYjLxyVwdkYMhh6Ylk0IgXlw\nzzwl2bGxgBFjBxAUbOyR/D0h447rKP92I1Ubd7L7/x5h/Et/V9OtdRGn08XW9XkATD59iG/FKBT9\nhA7DJIQQpwJ/kVLOdW/fA0gp5SNN0vwaGCCl/HN7eXUnTOLgv18ie+GiFvsz7ryBzP/7RYfp20rn\nKQUFBRQUFBAREcFbb73F4cOHeeyxx0hKSupynkuXLuWTTz7h/vvvJz09vcv5+CsqTKJn2F9az9vb\nilmbq/XA6QScnRHNFeMSGRId4mN1gYeUki1Ha3l3RzG3TBtEalSwryV5jNPp4sV/f8P86yYTn+Tb\nHsSGvCLWzVqAo7aeUY/ezaBrL/SpnkBl/85jfLxkGzHxoVx/+3T1p0Kh6AZeixkWQswHZkspf+Xe\nvhaYIqW8rUmaxwEjMAoIA56UUr7ePK9AjhletmwZ8+bNQ6/XprdZtGgRlZWV3Hnnnd3Kt7a2lrPO\nOotly5apmGFFp8itbOSdHSV8faiC4xNOTBscydXjkxgWb/atOEWvsH/nMbZ+n8uVv5rqaykAFH7w\nJTt+/QD6kGCmrXyN0PS+dU/rDd59eSN52eXMPH8EE6cN8bUchSKg8dQZ9tYoHAMwEZgJhALfCyG+\nl1IeaproiSeeIDQ09ERIQGRkJGPGjAmIXlGr1XrCEQY4cODACd1NwySa0laYxFdffcXChQtZvnw5\n4eHhxMfH8+GHH/Lb3/62d06ml6iurubw4cNMnz4d+DEWyl+3n3vuOcaMGeM3ejrazt+9mWl6WHD5\nKby3s4S3P13J8mzJutzxTE4JJ8uWQ1pMiE/0NY178xd7dXU7a8JUjHrBjk3rvZr/yvc/JCghtlv2\nXLviIBdeMsd/7BVvZsD88yha+iVvXncbWQ/dwRkzZviPvg7s6evtmmoLedkODEYdVY1HWLOmwK/0\ntbbd3Ka+1hPo28qe3bffmjVryMtzhxpNnsysWbPoCE/DJB6QUs5xb7cWJnE3ECyl/Kt7+yXgcynl\nSZNrLly4UN5www0tygiEHsQ77riDxx9/HIDy8nIuv/xyli1bRnh45x9Nrlixgg0bNnDfffchpWTs\n2LE88cQTzJw509uyfUog1GtT1qxZc+LCCkQqGuws3VnCx3vLTqy+NjYpjKvGJzIxObxXH7cGui2b\n8vn+cl764ShzhsUyf0wCMebux+Y2Hi1m3bnXc9rnL2Ie3PHKYm3Z0+lwIQTo9P4z5Z69qoY1Z/8M\na1Epw+77Nem3/szXklrgr+1z1Wf72LzmSEBNp+avtgxUlD29izfDJPTAfrQBdEXAD8BVUsq9TdKM\nAJ4C5gBBwAbgCinlnqZ5BWqYxM6dOyksLKS6upqQkBD27NnDNddcQ0pKSpfzXLRoEQ6Hg/z8fDIy\nMrjuuuu8J9hP8Pd67avUWBws213Kst2l1NmcAAyPN3PNhCSmDopQMYhdoKTOxv92lPB1dgWzhsZw\n+dgE4kK7N3tDzvNLKFn+LVPefwah8x9n1huUrlrP5qt+jzAZmfbFIsKzMnwtye+x25389+HVWBrt\nXPub00hKifS1JIUi4PHqPMNCiDnAE2hTsb0spXxYCHETWg/xC+40dwHXA07gRSnlU83zCVRneOnS\npcyfP9/XMgIOf6/Xvk69zcnHe0tZurP0xJLEQ2NDuHp8EtOGRKJTTnGnqWiw897OElZnV/LyZVmE\nGLu+RK50Ovnhkt+S+JMzGXLTlV5U6R/s/sO/yV/8AeGjMjnt85fQmXw320UgsGvLUZa/t5PE5Ah+\ndss0X8tRKPoEXp1nWEq5XEo5XEqZKaV82L3vv8cdYff2o1LKUVLKsa05whC48wzr+livjaJ1msYc\n9QVCTXquHJfE4itGcvOpycSYDRwqb+TBlTnc/P6+Hl3qua/Z8jgxZiO/mprMq5eP7JYjDCD0esY8\ncV3/9A4AACAASURBVB/ZTyym7uCRdtMGoj2H/+UWQgYPpHb3QbIff8XXck7CH+25fYMW4zh+amBN\ns+mPtgxklD19g/LyPODiiy/2tQSFosuEGPVcMjqBxZeP4rfTUogLNXKk0sI/Vh3hl0v3suJgRY85\nxX0VUxvLYnfWjuYhKWT+341kP+ZfzqI3MISaGfPEn0AIDj/5OlVb9nR8UD+lpLCGovxqgoINDB/b\n9ek6FQpF11DLMSt6DFWv/onN6eKrgxW8va2Y4jptqeeBEUFcPT6RWUNj0PfAohP9hYdW5qATcPWE\nJI/nfJYuFy6rHX2IZwunFOVXUVNlYfiYwHCa9v31aY489xahQ1OZ9tVrHp9nf+LLD3axY2MBE08b\nzMx5Wb6Wo1D0GbwaJqFQKPoOJr2On46I45XLR3LXjFQGRpgorLHy6Ld53PC/PXy+vxyH6inuEr8/\nI5WhsWbu/uwQf1uZw+Hyxg6PETpdpxzEH77NoaHe1h2ZvUrm3b8kbHga9YfyOPCP53wtx++wWhzs\n3V4EwNgpal5mhcIX9KozHKgxw4r+QX+L1TLoBOcNi+XlS0fyhzMHkxIZRFGtjce/y+P6d/fw6b4y\n7E5Xl/Lub7Y8jtmk5/Jxibx6+UiyEkK594tDPPZtXrfzPW7P2moL+YcrGDUhcJ646IODGPPk/QiD\nntwX36V8zWZfS/Kr9rlnWyF2m5OUtGjiEsN8LafT+JMt+wLKnr5B9QwrFP0cvU5wTmYML87P4p6z\nBjMoMojiOhtPrMnn+v/t4ZO9Zdi66BT3V0KMei4dk8Brl4/ip1mxXst356YCho9NwhRk8FqevUHk\nuBFk3H4dADtv/zuOunrfCvITpJRs/yEwB84pFH0J/QMPPNBrhTU2Nj4wYMCAFvtra2u7tHiFwr8J\ntHo9vjJif0UnBGkxIZyfFcfgqGDyqiwU1tjYkF/DVwcrMOm17z2JKe7vtjyOQSc6PR+xo74RS2Ex\nxqiIE/tSU1NxuSSfv7eTs+aOIDQ88OJuo04ZS+nKddQfzMVeVUfCuaf7TIu/tM/CvCp++CYHc6iJ\n8y4ejS4A4/X9xZZ9BWVP71JUVER6evpfO0qneoYVCsVJ6HWCszKi+e/8Efxp5hAGRwdTWm/nqXUF\nXPfuHj7aU6p6iruJS0qeWVfA/tKWPaRlq9azZcHdOC3Wk/bnZZcTGh5EwsCIFscEAjqjgTFP/Alh\nNJC/+APKv9vka0k+Z5t7OrUxk1PQtzFDiUKh6HlUzLBC4UbFap2MTghmpEfz30tG8KdZQ0iLDqas\n3s7T6wq47h23U+xo3SlWtmwfKWFQVBB/XZHDn77IZl/Jj05x4k/PIjRzMIceffnEvjVr1jB4aCyX\nLJjkC7leIzwrg6F33gDAzjv+4bNwCX9onw31Ng7sPAYCxk7p+mqmvsYfbNmXUPb0DeqvqEKhaBed\nEMxIi+a5S0Zw/6w00mOC/5+9Mw+Pqjob+O/OPlkm+wIhhCwEAiQEDJssgiiLGiil1A1bxc/1U7vo\np221aittta20brV1wbqAigtSl0oVKcpqWEISQggQyJ6QfZJJZr/fH5PEAAGyTGYy4fye5z4z595z\nz3nve++dee973/MealvbjeIN5zeKBd2jVEgsGRfBP384jmmxBn67xWUUH61tRZIkxj35AOXvfkbj\n/kOd+0iShF9A/6aAHgzE37MSQ9pYzGVVHPntC94Wx2vk7SvH4ZCJT44gKMTP2+IIBBc1Is+wYMAQ\n53Vo4pRldp5s4q0DlRTVmwEI91NzXXoUi5LDzjkhheDcWB1ONh+pw6BTcVlCCACVH33Jsadf5dIv\n/olS53sxwuej+fBxdi5chWy1kbHhGcLnTPG2SB5Fdsq8uuYbGutbWXbTZBJTIr0tkkAwJBF5hocg\nO3fuxGw2Y7FY2LVrl7fFEVykKCSJWfHB/G3ZWB694nRP8Y835LPpkPAU9xaNUkHmuIhOQxggeul8\nApLjqf73Ni9KNjB0DZfI+9nvsTdfXNklSorqaKxvJTBIR/yYCG+LIxBc9IiYYR/i7rvvJiYmhokT\nJ9LQ0OBtcYYcIlardygkiVmjTjeK61ptvLCrjMzV60T4RD+RJImJL/6GiCVX8PYnX3pbHLcT/783\nYpg4FnN5NQW/fd6jfXv7Xj/4bSngGjjnixkkuuJtXQ41hD69g28lqxwE5OTkUFxcDMDJkye59957\nPdb3z3/+c+bPn090dDRKpdJj/QoE56PDKL40LoidxU28tb+K7ON2nt9ZxjvZ1SJ8oh8oNGq27zjJ\nG1nl5KmOs3JyNCmR/t4Wyy0oVK7sEjsX3ELZm5uIvmYe4ZdN9bZYA46p2cKx/FNIConUDN8dOCcQ\nDCU8+u+Unp7uye7cTm5uLkajkczMTDIzM/nyS896a9RqNTExMcIQHiBmzZrlbRF8mu88xWP48x3L\nSAjVi4F2/cTY2EbOV8d5/xc3MH2kgSe2nODhz49z+NTQCCsIHJtA0gO3ApD38z94LFzCm/d63r4y\nnE6ZxLERBAbpvCaHuxC/m+5F6NM7CM9wLygoKGDFihWAK+QjJSUFcHmI33jjDSRJomNAYsd3SZLI\nyMhg8eLF/e5///79yLJMfX09iYmJbmlTIHA33XmKi+rbOj3F106MYvEY4SnuCTlZZaRMHIa/Xk3m\nuAgWjglj85E6Vm85wS/njWJCtO9N33sm8XffwKnPttGUfZiCx59lwtO/9LZIA4bslDmYVQbAxKmx\nXpZGIBB04NFsEk8//bS8atWqs9b3JOvAji+Psuur42etn3F5IjOvGH3B+ueq11PKysooKyvDYDCw\nfv16ioqKWLNmDdHR0X1us7fk5OSQlpYGwJw5c/jkk08wGAZvAn5fyyaxfft28VTuJrrq0inLpxnF\nAGF+aq4TRvF5cTqcvPSnbSy/OYMjxw4ya9YsmguK8IuLwaFRo1ZISJJvx5t20HLkBDuuvBnZauOS\n9WuIuHz6gPbnrXv9RGENH/xzH4YQPbfdPwfJx+OFQfxuuhuhT/fS02wSPuMZnnnF6F4Zs72tfyH2\n7t1LZmYmSqWS1atXs3btWtatW8f999/fr3afffZZzGbzaes6PMrXX389sbHfeQ8mTJjQ+T04OJjt\n27dz1VVX9at/gWCg6eop3lXcxJvtRvELu8p456DLU3yVMIrPouhIDYZgPRHRgRw51r7umdfRDYtk\nzKP/2+0+TllG4YMGcsCYeEY/eBuFq/9G3v1/YNZ/30Id5DtTufeUjoFzaVNGDAlDWCAYKnjUGPbl\nmGGLxXJarG5hYSEJCQnA6WESXelJmMR9993Xo/7fe+89vvjiC1566SUATCaTiB12M+Jp3H10p0uF\nJDFzVDAz2o3itw5Ucbyujb/tKuOdg1VcmxbFVWPD0QqjGHAZTmntr9I79JnyxE/ZcfmPiFw8h5Ap\nqWft82FeDfvKjKycHM34KN8KoYi/63qq/72Npn2HKHj0GVKfeWTA+vLGvd5iNHO8oAaFQiL1kqEz\ncE78broXoU/v4DOeYW+ze/durr32WgDq6urIysri4YcfBmDUqFE8+uijA9p/bGwsN998M+AyhOvq\n6pg9e/aA9ikQDAQdRvGlcUHsKnF5io/XtfHi7nLePVjNirQork4JR3eRG8VzFo0hOPT0mck04SGk\n/OF+cn+ymplfvo7S7/QBWEvHhaNXK3hyazExQVpumhTNeB+JK5aUSld2iSt+TPm7nxF19TwiF8z0\ntlhuI3dvGbJTZvSEKPwDh9YkKgKBryPyDPeA3NxcFi1axIYNG/j444955ZVXeP311wkM9NxrvOnT\np1NeXs6LL77I6tWreeWVV/DzE1N4uhOR39F99ESXkiRxaVwwf/veGB6/Mp6kMD31bXb+saecH797\niPdzqmmzOTwg7eAkIjoQtcb19qerPqOvnktQegqFv3/xrH3USgVXjw1n7YoULosP5qltxTz02VHM\nPpLFIyApjuRf3gnAoQeexNpgHJB+PH2vO50yOUN04Jz43XQvQp/eQXiGe0BhYSHLly/vLGdmZnpF\njo5MFgLBUKLDKJ4xMog9pUbe2l9FYW0rL31bwbs5p1iRGknmuHD0ahEW1EHK737OniV3Yq1tQBMe\nctZ2tVLB4rHhXJkcxr4yo0952eP+ZwXVn22jYc9BDj+yhokvPO5tkfrNicIampvMBIf6MTIhzNvi\nCASCM/BoNoktW7bIkydPPmv9YM86sHHjRpYtW+ZtMXyOwX5eBYMTWZbJKjPy5v4qjtS0AmDQKlme\nGsmScRH4a4RRDOC021GohqY/w3SijJ2X/whHm5lJa/9A1FWXeVukfvHhG/soKqhhzqJkps5J8LY4\nAsFFQ0+zSfiOu8CLCENYIPAckiQxNTaIZ5ck8/tFiYyL9MdocfDa3kpueucQb+6vpNli97aYXqe/\nhvCmQzXsLTPiSYdIT/GPH0HyI3cDcOjBP2Kta/SyRH3H2NjGiSM1KJQS4yfHeFscgUDQDSJmWCBo\nR8RquQ936FKSJDJGGPhL5mieWpxEanQALVYHb+6v4qZ3DvHa3gqM5qFlFDc1tFFb3XLW+oG4NkP8\nVPxjdzn3/auQ3SVNg84oHnnL9wm9dDLW2gbyf/m0W9v25L2eu7cMWYbR46LwDxh6A+fE76Z7Efr0\nDsIzLBAIBjWSJDEpJpCnrxnNn69OYtLwAFptTt7Oruamdw/xyrflNLTavC2mW/j26yIK86o80tec\n+BD+sXwsK1Ij+efeCu7+6AjbTw4eD6ykUDDhL79C6aen6l9bqPzoC2+L1GucDie5e9sHzk0bWgPn\nBIKhRI+MYUmSFkmSVCBJUqEkSQ+dp94USZJskiR9v7vtvpxnWDD0Efkd3cdA6TJtWCBPXTWav2SO\nJmNEIG02JxtyTnHTu4f4264yakzWAenXE1jMdo7kVJE25ewctBfSpyzL1G3f2+s+FZLEnIQQ/rZs\nLD+aPIyT7TMEDhb84oYz9jf3AnDooT9jrjjllnY9da8fP1JDi9FCaLg/sfGhHunT04jfTfci9Okd\nLmgMS5KkAJ4HFgLjgeslSRp7jnpPApvdLaRAIBB0ZXxUAL9flMRzS5OZEReE1SHz0aEabn43n2e2\nl1DZbPG2iL3m0IFyRiaGEWDQXbjyGTjbLBx64CmqP/+6T30rJIkZcUGsnDysT/sPJCNWLiXiypnY\nm5rJ/clqZKdvpIkDOLCzGIC0qbFDZupsgWAo0hPP8FTgqCzLxbIs24B3gKXd1LsXeB8456O7iBkW\nDGZErJb78JQux0T485srE/j7srFclhCM3SnzaUEdt2zI50/biilpNF+4kUGALMtk7y5h0vSR3W6/\nkD6VfjpSn3mE/Af/hKWm3u3yZZUasXopV7EkSUxY80s0YcHUfbOX4lfe63ebnrg+a6qaKSmqR61R\nkpoxdAfOid9N9yL06R16YgzHAKVdymXt6zqRJGk48D1Zll8ExOOvQCDwKAlheh6+PJ6Xf5DCFaNd\nr6O/OFrPbe8f5oktJzha2+plCc9PaVE9kiQxIv7snME9JWTaRGKuv5q8n/7OrYPhHE6ZTwpq+dGG\nQ7znpYlQtBGhjH/6FwAU/u5FmguKPC5Dbzmwy+UVHj85Bq1O7WVpBALB+XBXksq/Al1jibs1iI8d\nO8bdd9/NyJEu70dQUBCpqakkJIi8i0ORpqYmioqKOmOgOp54B2u5Y91gkceXy7NmzfJa/w9eNoub\nJkXzx3WfklVq5Bsm8s2JRoYZC5mfFMqPllzpdf2cWQ6LDCB0ZAs7duzolz6dM1JQ/fdbSl77kNLk\nKLfJ95srE9jw2Zds+W8BG3LGsnRcOJFNhfiplR7T19EABTXzJhKx9SA59/wGx8O3oFCrBuX12dZq\n5bNPvsBhl7lluvevL1EW5Yul3PG9pKQEgIyMDObPn8+FuOCkG5IkTQcel2V5UXv5F4Asy/JTXep0\nPKZLQDhgAm6XZflfXdvy1Uk3BH1DnFeBt6kz2fgg7xSfHK7tnJJ4QpQ/16VHMWWEYUjGcZqOl5D/\n8Boy1q9BUrg/YVBZk5l3D1YTqldzyxTP3t/2FhM75v+YtuIK4u9ZyZj2XMSDjW+/LuLrzwsZNTqc\nH9yS4W1xBIKLFndOupEFJEmSFCdJkga4DjjNyJVlOaF9iccVN3z3mYYwiJjhM8nLy+PXv/71Rdv/\nYKPrk6WgfwwWXYb5q7l9WgxvXTeelZOiCdQqyas28cjmIu7aWMDW4/U4nIMrv2539Eaf/okjmfLO\nXwfEEAYYEaTj/jlx3Jzh+cF2qgB/0p5/DBQKTrywjvrdfftPGcjr0+lwcmC3yys1+dK4AetnsDBY\n7vWhgtCnd1BdqIIsyw5Jku4B/oPLeH5VluXDkiTd4dosv3TmLgMg56AhJyeH4mJXLNjJkye59957\n+9TOCy+8wJ49ezAYDO4Uz2f6Fwg8iUGn4keXDOMHqZF8UlDLh3mnKKo384etxby2t5IVqZEsSA5D\nqxKp13vKubzqZU1mRgT1PiNGTwmZkkrCfTdR9NfXybnnt8za+iaqQP8B66+3HDt8iuZGMyFhfsSP\nDve2OAKBoAdcMEzCnfh6mERubi5NTU2dMSpLly5l06ZNfW7v7bffZseOHTz//PPuEnFQ9e8r51Vw\n8WF1ONlytJ4NOacoN7rSsAXrVCybEEFmSjgB2gv6CQTd0NBq4+6PjhAfquOHaVFMHBYwIKEoTpud\n3VffjjGngOE/vIq0Zx9xex995Z2X9lB2soHLr0m5KDzDAsFgpqdhEj7xi7/glQNuaec//zOpX/sX\nFBSwYsUKwBXykZKSArg8xG+88QaSJHWO4u74LkkSGRkZLF68uH/CX4DBIINA4CtolAoWjw1nQXIY\nO4obefdgNUdr23htbyXvHKzmqjFhLJsQSWSAZkDlqCprIipm6MQuh/ipef3acWw51sCzO0rx1yhZ\nkRbJzLhglAr3HaNCrSLthUfZueAWKjZ8RvhlUxi+fKHb2u8rpyqMlJ1sQKNVMn7y0E2nJhAMNTxq\nDGdnZ9OdZ9gXKCsrIzY2lvz8fNavX09RURFr1qwBYNSoUTz66KMD1ndVVRXr1q0jNTWVnTt3cuut\ntxISEkJrayuRkZEekeFioGsmCUH/8BVdKhUSc+JDmD0qmOyKFt45WM2BimY+yKvho0M1zE0MYUVq\nFAlherf3farSyEdv7ef2/7sMSXl+Q7E/+rQ3myh/9zNG3voDjxjdGqWCxWPCWJgcyq7iJjbkVNPQ\namfp+Ai39hMwehQpT/yUQw88xaEH/0RQegr+id3naT6Tgbo+97enU5sweQRanU/4mvqNr9zrvoLQ\np3fwibu1vx5dd7B3714yMzNRKpWsXr2atWvXsm7dOu6///4B7be1tZWVK1eyYcMGQkNDCQ8P55FH\nHmHFihUsXOh9T4hAMBSQJIlJMYFMignkWG0r7+WeYltRA1uOuZZLYgJZkRbJpOGBbjMoD+wqYeLU\nWBTKgY1TllQqSt/8CKWfnhE3XDOgfXVFIUnMHBXMpXFBDNQYxRE3LqFu+z6qPvqS7Nt/zfRPX0Kp\n0w5MZxeg1WTl8MFKkGDSjJ4Z5QKBYHDgUWM4PT3dk925FYvFglKp7CwXFhZ25kfuGqLQFXeEKGzc\nuJH09HRCQ10TCURERJCfn48sy6jV3yVyH0gZLhbE07j78GVdJoX78ct5o7glYxgb82r495E69pU3\ns6+8mcQwPcsnRHJZQjDqfhixLUYzRw9Vs+pns3tUvz/6VOq1TPzHE3z7/XsImpRCYEpin9vqC5Ik\n0Z3j2+GUqW6xMtzQd+NVkiQm/OkhjAcLaD50lILHnmX8U/93wf0G4vrMySrFYXeSMCaCkPDBM6Bv\noPHle30wIvTpHXzCMzwY2L17N9deey0AdXV1ZGVl8fDDDwP9C1E4cwBjUVER8fHxnUatzWY7bVIS\nk8mEQqEgMzPztP36KoMnB1AKBL5EdKCWu2aM4MZJ0XxyuJZN+TUcr2vjj9uKeTWrgqXjw7lqTDiG\nPrwO37ejmHHpw/Eb4JjkDgLHJjD2sXvIvu1hZnz+KqoA7xtr5UYL939ylPFR/qxIjWRclH+fvO6q\nQH/SX3qCXVffTunrGwm9dDLDll44yb47cTicZF9E6dQEgqGG8vHHH/dYZxs3bnx80qSzQx6am5sJ\nDAz0mBy9JTc3l6ioKPbv309RURGbN2/m0UcfJSKi7zFwL7/8Mhs2bODQoUM0NTUxceJEtFotixYt\nIikpifj4eAASEhLYtm0bFouFwsJCLBYLp06doqWlhaSkpNO8w+7o350M9vN6Jtu3b++cHVHQP4aS\nLrUqBanDAlg6LoJhBi2VRguVzVYOVLSwKb+WhlYbMQZdj41ic5uNz9/PZdEPUtHpe3b/ukOfhgmj\nac47StWn/yXq6rleH7QXpFORmRJOm83Jq1kVbD3egF6tZESwDkUvZdNGhaMOMlC7ZRd1274lesnl\nqIPPnTbS3ddnYV4VefvKCY3wZ+5VY72uW08ylO71wYDQp3uprKwkISHhNxeqJzzDPaCwsJDly5d3\nls/0yvaF2267jdtuu+2s9bt27WLHjh2dZYPB0OmB7mDu3LkD1r9AIOgejUrBwuQwFowOZV95Mx/m\nnWJvWTOb8mv5V34t00cG8b0JEaRfIJ2YUqng6mvTCApx/6C8C5Hyu59z8qV3kB0OJJX3f/71aiVL\nxkVw9dhwdpU0sTGvBqcsc3lSaK/bGnnL96nfsY/qT/9L9u2PMv3jv6PQesbzfqB94NykGXEXlSEs\nEAwVRJ7hHrBx40aWLVvmsb4WLVqEXu/5P0p3M9jPq0DQX07Ut/Fh3im+OtaArX2UWHyIju+Nj+Dy\npFAxiUcf6Bjn0BdsTc3svOJm2koribvth6Q88VM3S3c2FSWNrP/7bjRaFXf+Yi4akaNaIBg0uHM6\n5oseTxnCAAsWLBgShrBAcDEQH6rn/jlxvHX9eH50yTBC9SpONJj5y/ZSbnw7j9eyKqg1Wb0tpk/R\nnSFstjvZW2bEeQHnjTookIn/eAJJpaT45Q1U/3vbQInZyc6vjgGQPj1WGMICgY/iUWM4O7tv88hf\nTPj7e39gy8WKmBPefVxsugzRq1k5KZo3rxvPg5fFkRzuh9Hi4O2D1ax85xCrt5wgp7KlzwNWLzZ9\nnkmtycor31bwP+8fZtOhGlqtjnPWDZ48juRH7gYg977VtBSePKuOu/RZWdrIycJa1BolGbPi3dKm\nr3GxX5vuRujTOwjPsEAgELgJtVLBFaNDeW5pMn+5ZjRz4oMB+PpEIw98epQ7Pyzg04Ja2mznNuY8\njdNu97YIF2REkI4Xl43hZ7NHklvVwk3vHuKFnWVUNlu6rT/qjuuIzrwce7OJ/Tc/hK3ROCBy7frq\nOADp00fi5++Z+GSBQOB+RMywYMAQ51UggBqTlU8P1/LxoRqabU4A/DVKFiaHkpkSTkyQzmuyybLM\nnsw7SP7VXYRe6v3JjXpKjcnKJ4drmTQ8kPTh3WessZva2LPkTpoPHSV83jQueevPSF1yxfeXqrIm\n3vrbLlRqJbf/32UeS5MnEAh6jogZFggEgkFAhL+G2QEqrmk28dDcOMZF+mOyOvgwr4Zb3jvMQ58d\n45sTjdgHapq28yBJEkkP3kb2Hb+m9WSZx/vvKxH+Gm7JGH5OQxhA5a9n0mtPog4NpnbrHo6sftGt\nMuzqEissDGGBwLcRMcMCQTsiVst9CF2ezrfbipgxJ575SaH8dUkyz39vDAuTQ9EqJQ5UNPPElhOs\nfCeP1/dVcqrl7AF3A6nP8DlTSLp/Fftu+j9sxpYB68dTNLbZ+MPWk+RUNqOPjWbSK79DUik5+eJ6\nKt7/HOi/PqvLmzheUINKrWDKRRor3IG4192L0Kd3EJ5hgUAgGEDKTtRjaraSPCG6c11yuB/3z4lj\n/Q0TuGt6DLFBWupb7aw7UMWP3j3EY/8pYk9JEw4PeYtH3vx9wmZP4eAdv/aJGOLzoVUpSIn055nt\npfzP+4fZGhhD/GM/ASDv/idpOpDf7z46YoUnThuJf6B7JysSCASeR8QMCwYMcV4FAvjg9X0kpUQy\ncWrsOevIskxuVQsfH65lx8mmzpCJcD81C8eEsSg5jKjAgX0V77Tb2bfyAeJuWU7kwtkD2pcnkGWZ\nvGoTnxXUsrvEyO3ffIT08edoo8OZsXktuqjwPrV7qsLIG8/vRKVScNv/XSaMYYFgENPTmGGRFFEg\nEAgGiJqqZk5VGFl6Q/p560mSRNqwQNKGBdLQamPz0To+P1JPhdHCugNVrD9QxSUjAlk0JowZI4NQ\nK93/Uk+hUnHJm39GoR4afwuSJJEaHUBqdABGsx1zZiInaipp2H2Q7Ft/xdQPnu/TDHXfeYVjhSEs\nEAwRRMywl/j888957733+OMf/8irr77qbXF6zPvvv8/zzz/PqlWr+OCDD7wtjlsRsVruQ+jSRVhk\nAD+8dQoqdc+zGIT4qbluYjRrV6Twx6uSmJcYgunEQfaWNbN6y0luePsQf99dxon6NrfLO1QM4TMx\n6FREhviT/vLv0MVEsfPbPeT+9HfITieHqlt6HI5SU9nM0fxqVCoFU2Zf3LHCHYh73b0IfXqHofnL\nN4Dk5ORQXOyah/7kyZPce++9vW7DaDSyatUqTpw4gUajISkpiQULFhAbe+7XqIOBEydOUF9fzz33\n3ENdXR0ZGRlMmTKFkSNHels0gWBQolBIhEUG9G1fSSK9PXXYZDme1sgYPjtSR3GDmQ/zavgwr4bR\n4XoWJocxNyEEg078nF8IbUQok19/iuyrb6Jy4xcog4N4efpVVJtsXDk6jEXJoedNdbdrqyuDRNqU\nWAIM3kuJJxAI3ItHPcPp6ed/VTjYyc3NxWg0kpmZSWZmJl9++WWf2jEYDGzZsgWtVoskSTgcjj7P\nTOVJCgoKeO655wAICwsjISGBAwcOeFkq9zFr1ixvizBkELp0Lwsvv4xlEyJ56ftjeXZJMteM/YeM\nSAAAIABJREFUDcdfo+RobRvP7yzj+vV5/G7LCbJKjR4bdOerGCYkc9O6F5A0aspee5/7TuzmycVJ\nOJwyP/v4KD//uJBtRQ1n7VdT1UxhXjVKlYKplwmvcAfiXncvQp/ewSdcCZ9HX+qWdhZV7ezX/gUF\nBaxYsQJwhXykpKQALg/xG2+8gSRJnUZtx3dJksjIyGDx4sWntdWx765du7j00kv77V3tiwy95cor\nr+Tdd9/tLFdVVZGQkNCvNgUCQc+RJImxkf6MjfTnjukx7CxuZHNhPQfKm9l2opFtJxoJ0auYlxjC\nFUmhJIbpkaQLjh05J5aaevJ++jvS/vY46qBz5/T1NcJmZTDxhcfIvv3XHH3yJcaHh3D7yqXckjGM\nb0uNtLVPjtKVjljhtIwRwissEAwxPGoMZ2dn0102CV+grKyM2NhY8vPzWb9+PUVFRaxZswaAUaNG\n8eijj/a6zQ8++IBPPvmE1atXn7deVVUV69atIzU1lZ07d3LrrbcSEhJCa2srkZGR/ZKhN6hUKsaN\nGwfA5s2bmTRpEqmpqQPapyfZvn27eCp3E0KX7qU7fWpVCuYlhjIvMZRTLVa+PFrPl8fqKWuydIZR\nxIXouCIplHmJIUT2YWIITXgIfgmx7Fv5ABnv/BWVv95dh+RVtm/fzqzMyxn3ZBP5D/2JQw/+CXVI\nENFXz2XmqOCz6peeqKcwrwqlUsHUy4QDoCviXncvQp/ewSc8w/316LqDvXv3kpmZiVKpZPXq1axd\nu5Z169Zx//3397nN5cuXs2DBAubOnctHH33Ubcxwa2srK1euZMOGDYSGhhIeHs4jjzzCihUrWLhw\nYX8OqZNnn30Ws9l82roOj/L1119/llxGo5G3336bv//9727pXyAYSuz+73GGjQgmLinMY31GBmi4\nYVI016dHcaSmlS3H6vlvUSPFDWZezapgbVYFacMCmJsYwuxRwT2OL5YkibG/uY+8n/+BA7f8gslv\n/BGlbuhkUBj542VY6xo59seXOXjXY6jf/gthM0932DgcTr7c5MpNbIoN5v4vTzAvMYR5iSFEi2wS\nAsGQwKPGsC/HDFssFpRd5rUvLCzsDBHoGqLQlXOFKHzxxRc8/fTTfP755wQGBhIREcGmTZu45557\nzup348aNpKenExoaCkBERAT5+fnIsoxare6s11sZunLffff1ShfPPfcczzzzDAEBAZSWlg76gX89\nRTyNu4+LVZeN9a3s/eYkN/9kplvb7ak+Tw+jGEFWqZEtx+rZVdLEwcoWDla28PyOUjJGGJibGMKl\ncUHoL5DpQlIomPD0L8i+41EO3vUY6S+vRqHyCT/KOemqz8Sf3Yy1pp6S1z5g/48fZNrGFzCkjunc\nvn9nMXWnWggO9eNHN0+msN7MV8cauHdTISOCtFyeGMLiseGoFH0PR/FlLtZ7faAQ+vQOPfpFkyRp\nEfBXXAPuXpVl+akztt8APNRebAbukmU5152Cepvdu3dz7bXXAlBXV0dWVhYPP/ww0PsQBUmSmD3b\nldRelmXKy8sZP348AEVFRcTHx3catTab7bS4XJPJhEKhIDMz87Q2PREmAfDyyy9z9dVXY7FY2L9/\nP2azecgYwwJBf9n27yNcMnPUoIgpVSkkZsQFMSMuCJPVwY6TjWw93sCBimb2lBrZU2pEq5SYPjKI\nyxJCmBJrQKvqfky1pFQy8W+Ps//mX1C3LYuI+TM8fDQDhyRJpPzuZ1jrG6natIW91/+cqRtfIGD0\nKIyNbezc4sogcXlmChqNignRAUyIDuCuGTHsK29mX1kzyovTDhYIhgwXnIFOkiQFUAjMByqALOA6\nWZYLutSZDhyWZbmp3XB+XJbl6We29fTTT8urVq06q4/BPlNZbm4uFRUVNDU1odfryc/P58Ybb2TE\niBF9bnPt2rXY7XZKS0tJTEzk5ptvBmDatGk8+eSTzJs3D3CFJDz33HNMnToVu92OXq9n3bp1zJs3\nj2XLlqHXey6Gb/fu3VxzzTXAdx7nnJycc567wX5ez0TEarmPi1GXpSfq+WxDDqt+Pht1L/IK9wR3\n6rOhzcY3Jxr56lgD+adMnet1KgXTRhqYE+8yjHXdGMay04mk8GgSogGhO306rTb23fQAdduy0IQF\nk7HhGbZmt3D0UDWjx0ex9MZJveqj2WJHIUn4a9x7LQw2LsZ7fSAR+nQv7pyBbipwVJblYgBJkt4B\nlgKdxrAsy7u71N8NxPRO3MFNYWEhy5cv7yyf6ZXtC909FIAru8SOHTs6ywaDodMD3cHcuXP73X9f\nmD59OrW1tV7pWyAYzMhOmf9+VsCchcluN4TdTYhezZJxESwZF0F1s5VtRQ18faKRwtpWthU1sq2o\n0WUYxxqYnRDMlBGGzlCKoWAInwuFRs3k157iwK2/pHbrHr68688UzVqGWqNk3tVje93evrJm/rq9\nhInDA5k9KpjpIw0EaH07vEQgGKr05M6MAUq7lMtwGcjn4n+Af3e3wVdjhhUe/APYtGkTixYt8lh/\ngu8QT+Pu42LTZVurjegRQYydOGxA2h8ofUYFavjhxCh+ODGKymYL35xo5JsTjRypae1M1aZRSlwS\nY2DmqCCmjwwaEpN7nEufSj8dk//5FPvufJwj/hMASE/SYwju/Ru4uYkhZIwIZGdxE1+faOD5naWM\ni/Ln5ozhJIf79Uv+wcTFdq8PNEKf3sGtv2qSJM0DbgG6PZvvv/8+r7zySmdO3aCgIFJTUwd9rtpl\ny5Z5rK8FCxZ4NPRhIGlqaqKoqKjz5u6YZlKURXmolf0CNOjDGtixY8egkKcv5eMHsxgOPLd0FlXN\nFl758D/kVrXQEDaWXSVNbN66DYUEM2fOYuaoYJQVeYTo1UwaNhJdTBS79mYNquPpT9ly/Y85tu5T\n1JWHMb+zk9oRv6dAZetTewtmzWJBchhfbv2agpoK/NWxXj8+URbloVru+F5SUgJARkYG8+fP50L0\nJGZ4Oq4Y4EXt5V8AcjeD6NKAD4BFsiwf764tX40ZFvQNXzuvIlbLfQhduhdv6rPOZGNncSM7ips4\nWNGMo8tfRlKYnoTCPBKP5HH1Mw+gCezb1NOe5nz6bKgz8c9nduCwO5lqLaT1rXeQNGrSX3qCqEVz\nBkymD3JPkTosgNH9nCjF04h73b0IfboXd8YMZwFJkiTFAZXAdcD1XStIkjQSlyF807kMYYFAIBD4\nHmH+ajLHRZA5LoJmi509JUZ2FjeSVdbMsbo2joUlwqWJvPnPA8xMGcbM5AgmDQ88Z2aKwYwsy2z5\n12EcdifjJw9n9vKFFOidFL+8gexbHyb1+V8zfNkCt/drczipa7Xxh69OYnE4mTHSFZIycVgAGh/U\no0Dga1zQMwydqdWe4bvUak9KknQHLg/xS5IkvQx8HygGJMAmy/JZccVbtmyRu5uBztc8iIKeIc6r\nQDB0sdqdZFc2s7vEyO6SJmpNts5tGqVE2rAApowwMDXWQEyQ91PN9YQjuVV8/HY2Wp2KVT+fjX+A\nFlmWOfrkPyh65g0ARj90Gwk/vXlAvLeyLFPaZGFXcRN7SppwyvDXJclu70cguFjoqWe4R8awuxDG\n8MWFOK+CoYrT4WTX1uNMmROPRuPWoRc+iSzLFNW38dn729lbZ6My8vT7frhBy5QRBqbEBpI2LLDb\ntG3eprG+lbde2IW5zcYVS8aRPn3kadtP/G09R554AWSZ6MzLmfDXhwd8emq7U+52Mg+T1YFGKaFW\nDj49CgSDiZ4awx69k7Kzsz3ZnUDQK7oG4Av6x1DX5a6tx6koaUSt8kwatcGuT0mSSAzz4947FvDC\nDyfw7g0T+L/LRjI3IZhArZIKo4VN+TU8srmI5W/m8NBnR3n3YDVHa1txetAh08GZ+rRZHWx66wDm\nNhuJKZFMnHr2RELxd9/A5Df+iCrQn6qPv2LP0jtpK6saUDnPNavdl0frWfFWLo/9p4h/5ddQ3mQZ\nUDnOx2C/Nn0NoU/vIFwaAoFA0AvKTtSTk1XGTf87A+kinYL3fAQkxQFw5egwrhwdhsMpU1BjIqvU\nSFaZkWO1bRyoaOFARQuvZkGQTsWk4QFMjjEwaXggUYEaj8oryzL/2ZhHTVUzIWF+XLUi9ZznNfLK\nmUz/9GX2//hBmvOOsmvhKiat/QMh0yZ6VOal4yO4LCGYAxXN7C1rZn12FVqlgp/OHsmk4YEelUUg\nGAqIMAnBgCHOq2CoYW6z8fpzO7hiyTgSx0Z6WxyfpMls50B5M/vLm9lfYeRUi+207dGBGtKHBZI+\nPICJwwMJ81MPqDz7d57kq08KUGuU3HjXdMKjLmxM2hqNZN/xa+q2ZSGpVYz7w/3Erlw6oHKeD1mW\nOdlgJlinIqQbfTmcMkrx4Ca4CHFnNgmBQCC46OnwICalRApDuJfU7zqAQqslePI4gnQq5iaGMDcx\nBFmWKWuyuAzj8mZyqlqoarbyeXMdnxfWARAbpGXi8EDSogNIjQ4gzN99xnHpiXq2fnYEgEXLU3tk\nCAOogw1csu5pjjzxAsX/eJdDDzxF08ECxj5+34DHEXeHJEnEh56739s/OEyIXk3asADShgWQEunv\nk9k+BIKBQvn44497rLONGzc+PmnS2fO7Nzc3ExgoXu0MNXztvG7fvr1zQhhB/xiKupSdMk2NZmbM\nS0Th4YFLvq7P5sNFHLzj16iCAghK+25qY0mSCNKpGBvpz7zEEFakRjIjLojhBi0KCepb7dS32Sms\nbeWbk418kHeKLccaOF7XSovFgZ9aSYBG2evMDtu3byckKJL3Xs3CZnUwZU48l8wc1as2JIWCiHnT\n0cVEUbN1N8YD+VR9spWg9BR0wwfXw9KVo0OJCFBTabSwubCOl/ZUsL+8mflJoSj6mRXD16/NwYbQ\np3uprKwkISHhNxeqJzzDPsTOnTuZPHkykiSxf/9+ZsyY4W2RBIKLBoVSwbTLBvdsmYOVyAUzmbrp\nRbJX/Yra/37LuD/cjzYi9Kx6SoVEcrgfyeF+/DAtCrtT5kiNiYMVLeRVt3Co2kSF0UKF0cLmwnoA\nwvzUjI/yZ1yUP+Oj/EkM8zvnwLMOHA4n/1p/gFaTlZGJYcy+cnSfj23E9ddgSE0m557f0lJQxO7M\nO0n8yY9I/PkqFOrB8Rfrp1EyNTaIqbFBALTZHBTVt3UbOmF1ODFZHN2GWwgEQxURM+xDpKenU1pa\nSkREBGvWrOGqq67yaP+yLBMfH49CoaDjupk3bx5r167ttr44rwKBoCuONgvH/vwK5Rv+zYQ/P0Tk\nwtm9298pc7yujZyqFnKrWsiraqHZ4jitjlYpMSbCZRynRPozNtKPEP3pht0XHx3i4LelBAbruOnu\nS/EL6P+gPYfZwtGnXubk398GWcaQNoa05x4lYEx8v9v2JMdqW3nws2ME6VSdDxkpkf6MDNaJuGOB\nzyHyDA8QOTk5FBcXA3Dy5Enuvfdej/X9xhtvMH/+fKKjo1EqPZPSqSvFxcVkZWUxdepUFAoFn376\nKXPnzmXMmDHd1vel8yoQCDxH04F8HBYrodPT+9WOU5Ypa7RwqLqF/FMmDlWbKOsmzVhUgIaxEX6M\nifRHW1LPkR0nUaoUXH/HNKJjgvolw5nU7zpA7n2raSutRKHVkPyrO4m77YdICt+J0XXKMsUNZvKq\nWjh8ysThU62kRPrx4NxR3hZNIOgVg3IAXXZ2Nt0Zw75Cbm4uRqORzMxMAJYuXepRY1itVhMTE+Ox\n/s5Eq9Vy9dVXo9fraWpqQq1Wn9MQ9kXEnPDuYyjosra6Gb2fBv9ArbdFGRL67ErQpHFuaUchSYwM\n0TEyRMfiseGAK1tFfrWJ/OoWCmpaOVLTSnWLlepmC+X7ykhoNFFcno9u1hzeLmpitNFGcrgfo0J1\naNwQCx46YxIzv3qDgseepWz9xxQ89iyVH33J2Cd+QkhGar/b9wSK9gF58aF6MsdFAK4JQLrj1Y2b\nCUpMJznCn9HhevRqzztqhhJD7V73FQZHQNMF+POvPndLOw/8flG/9i8oKGDFihWAy7BPSUkBXB7i\nN954A0mSOsMHOr5LkkRGRgaLFy/un/C4nnBkWaa+vp7ExES3tNkb2aOjozv3e+2117jrrrv63b9A\nMBipO9XCe2v3suB740lMGVyDoQTnJ0inYkZcEDPiXB5fh1OmuKGNrZ8cpqHRhAycCPHDKik5eKSO\nfx9xZa1QKSTiQ3WMDvcjKcyPxDCXMdiX2fJUgf5MWPNLIhfO4tCDf6LpQD57rrmDYd9fQPLDd6GP\niXLnIXuEc8Vha5UKqlusfH2ikRMNZqIDNSSH+5GZEs7YSH8PSykQ9A2fCJMYDMZwWVkZZWVlGAwG\n1q9fT1FREWvWrDnNQBxocnJySEtLA2DOnDl88sknGAyGc9avqqpi3bp1pKamsnPnTm699VZCQkJo\nbW0lMrLvf/CNjY2sWbOG3/72t+etJ8IkBL5IQ52Jd1/+ltkLkhk/2XtvYi5Gjq15DUt1LUkP3Nrt\nALu+4HA42fxBHvnZFSiVEpnXpxMzOpzjdW0U1rZytLaVwppWyposnPlvqJBgRJCOxDC9a2n3lobo\nVT3OYGE3tVL03JucfPFtnBYrCr2WhP9dSfzdN6L007nlGAcLNoeTkw1mCmtbGRvhR2KY31l1ShrN\nGLRKgvVigJ5g4BExw27mo48+IjMzszNWd+3atTQ0NHD//ff3q91nn30Ws9l82roOr+z1119PbOx3\n04I6nU4U7XFnS5Ys4c477zznILrW1laWLFnChg0bCA0NZf/+/TzzzDOsWLGChQsXolb3/Yfotdde\nQ61Ws3LlyvPW84XzKhB0pamhjXdf3sO0uYndTskrGFis9U0cf+afVGz4N3H/80NG3Xl9v/L22m0O\nPn7nIMcPn0KtUbLspsmMTAzrtq7J6uB4XSuFtW0U1bVyrK6NkkYz3UUHBOlUxIfqiA/VkxCqJz5E\nz8gQ3Xm9yK0llRQ+8QJVH38FgG54JMmP3M2w713hU/HE/eXZ7aVsLWpAq5JIaNdfQqieqbEGArQ+\n8bJa4EOImGE3Y7FYThu0VlhYSEKCK81S11CDrvQkTOK+++7rUf/vvfceX3zxBS+99BIAJpPpvIPo\nNm7cSHp6OqGhLu9KREQE+fn5yLJ8miHcF9m//vprrrvuuh7J7UuIWC334Yu6bDGaeeelPUyZPWrQ\nGcK+qM++oAkNIuU3PyFu1Q84+uRLfDPzWpIeuJURNy7pdS5hq8XOxjf3U1pUj06vZvnNlzAsNhjo\nXp/+GiVpwwJJG/ZdbnSr3eXpPN5uHJ+ob6Oovo0ms53sihayK1o660q4Zs+LC9ERF6wjLkRPXIiO\n2GCXkew3chjpL6+mftcBCh59BmNuITl3P87xv/yThHtWMuz7CwZNKrbe0Ntr875Zsdw7cwSnWmwU\ntetzZ3ET46MCCOgmPL/WZCXUT93vfMi+wsVyrw82fO/O8xK7d+/m2muvBaCuro6srCwefvhhAEaN\nGsWjjz46oP3HxsZy8803Ay5DuK6ujtmzXWmJioqKiI+PP+3PwmazdRrrHfsoFIrOwX8d9EX2oqIi\ndLqh9XpPIPAP1LL0xklEj3BvdgFB7/GLi2Hii7+hKfswNV/t7rUh3NTQysdvH6SqrAn/QC0/uCWD\niOjeTwCkUSlIjvAjOeK71/2yLFNjchlyJzqWBjNljWYqm61UNlvZXWLsrC8BkQEaYoO1xAbriA2O\nZcTavxL25X+pfO51TEdPkvuT1Rz948vE33UDI27IHHLhE2ciSRJRgRqiAjWdsd3n4lefH6ey2Ups\nkEt/I9uXGXFBF8wnLRD0FBEm0QNyc3OpqKigqakJvV5Pfn4+N954IyNGjPCoHO+99x61tbWUlJSw\nfPlyMjIyAJg2bRpPPvkk8+bN66xrNBp57rnnmDp1Kna7Hb1ez7p165g3bx7Lli1Dr+/7q8dly5bx\n1FNPkZycfN56g/28CgSCoYUsy+R8W8p//30Em9VBUIieFaumENxN7Kq7sTtlypvMFDeYKW5s/2ww\nU9ZkxnGOv9lAJUwp2M/YL/6NrqICAEVIMLG3/oCk21agDvKdGTwHEpPVQWmjmZJGM6WNZsqaLDwy\nP/6svMdOWSavqoWYIB2hvYjrFgxdRMywG/nggw9Yvny5t8U4J06nkx07dnR6igcLg/28CgQC36Vs\n/ScEXzK+c1ILY2Mbmz/Mo/iYKztE8oRorlgyzi0TavQHu1Om0mihtMlMaaOF0kYzpU1mShotmKzt\nE4Y4nSQV5DB123+ILnflsbepNVRlTKVtweUYMlIZHqRjmEHL8EAtoX7C0OsOk9XBw58fp9xoweZw\nMtygJcagJT5Uzw2TPDfYXTB4EDHDbkQxyAc3bNq0iUWL+pc2TiBitdzJYNal7JTJ2n6S0eMjCQnz\njdRPg1mf3sJaV8+3P7gX/zHxWC5fTPYpNVarA72fmvlLxjE2bdg59/WkPlUKqT08Qgdx362XZZnG\nNjvlRotrmTSM0qsu49i3B4j77FNijxUQu2s77NpOQ1gk2ybPIH/yNEyBQWiUEpEBGqIDNUQHaIlu\nDzmICnAtwR70ig6ma9Nfo+SvS1xvLI1ml24rjV0eOs6gzmRjQ061S4+B2vZPjVdzJQ8mfV5MiJjh\nHrBs2TJvi3BeFixY0K+wB4HgYqGkqI5vNheiUEikTDy3sSQY/CTc+yNCr13Kp6/tprJMBhxEOZv4\n/k++NygmSrkQkiQR4qcmxE/NhOiA7zZckYD8y+9TcegkJ9Z/TMum/xBSd4rZX2xi5paPKRsznpy0\nKZwcPY6yJj3QfFbbaqVEpL+GyAA1kQGaziXCX024v+tzqE+OYdCpMOhUpJwn17FSARH+asqNFvaV\nN1NptFDdYmVCdABPLk46q77F7sRidxKoVQrP/BBDhEkIBgxxXgWDharyJrb/p5CG2lZmXjmalLRh\nSGLwjc/S1NBK1jcnydtbht3uRKdXc9nckUTZaom8fIa3xXMrTrud2q17KH/nU05t/gbZ7vJySmo1\nyoyJtE2bQlVaOhVqf6parJxqsdJs6d4T2hV/jZJwf7XLQPbTEOavJsyvffFXE+6nJkinOisud6jj\nlGXabE78NWc/LORUtvD4F0XYnDIR7bqL8NeQOiyAhcndp+wTeJdBGSYhEAgEnsbcZuPjt7PJmBVP\nWsYIlH2YUUwwOKipaubbr4soyKlCbk8AnDwhisuvSSHAoANGd7tf/a4DWGsaCJs7FbUhoNs6gxWF\nSkXklTOJvHImlpp6Kjd+QfVn/6VhTw72XXtR79pLLDBh8ngiF80mfO401Mnx1LY5qW6xcsrkMpBP\ntVipNdmoMdmoNVkxWR2YrA6KG8zn7luCEL2aUD8VoXo1oX5qQvQqQv3UhOpd34P1aoL1KvzUiiHh\nLVVIUreGMEDasAA+/FEabTYHNS02Tpms1Jhs+J/Dy55VamR9dhXhfi7duRYV8SF6ksIHflCnoOd4\n1DP89NNPy6tWrTprvfAgDk187byKWC33Mdh06XTKKHzYwzXY9Olpyosb2LOtiKKCGgCk9jCXqXPi\nCY+6cMaFmq92U/zKezR8e5CgtLEUJ4Sz4MYfEpiajELlmz4hS009NV/spPrzr6n7+lucZmvnNlVQ\nIKHTJxJ66WRCL51E4LgkpC556WVZxmhxUNtuzNWabNS12qjr+Gxfmsz2C8phPJ6NITEdjVIipN0w\nDtapCNarCNJ9t7jWu7zNBp0SnWpoGM/nw2i2c7KhrV2fdupbbdS32kgK9+MHqWfPAnugopnXNv6H\nSVNnuPTVrs8Yg5ZILw8E9VV8zjPcdXY1ge/jdDq9LYLgIsPUYsFqthMSfnaMoC8bwhcrtdUtHD1U\nReGhamoqXXGxKpWC1IwRZMyOJyik5+MkIi6fTsTl07Gb2qjfsY/CN98h92e/Z8xj9xAxb/pAHcKA\noo0IZcQN1zDihmuwm9qo2/YtpzZ/Q/3OA7SVVnJq83ZObd4OuIzjkGkTCUpPIWjiWAxpYwiKCCVI\np+IcE/IBYHU4aWxrN+LabNS3G3QN7d8b2mwcq1CjVEpYHDLVLVaqW6znbrALaqVEkFbVHturJEir\nIlCnIlCrJFCrwtD+6SorCdCqCNQo0fjQmx2DTnXaJC4XItJfw8gQHRqVgnKjhfxqE41mO5eMCOS6\niWdnw8gqNbKjuLFTjx0PGrHtmUcEPWdQxAxbrVaqq6uJiYkRBvEQwOl0Ul5eTlRUFBqNeJoVDBx2\nm4PjBTXkHyin7GQDMy5PImPWKG+LJegDsixTU9lM4aFqCvOqqK8xdW7T6lRMmj6SSZfG4d/dNGVu\n5tjTa9GEBWNITSZgbGK/poT2Bq0llTTsOkD9zv2dxvGZ6IZHYkgbgyFtLIYJyQSMGYV+RPRpHuTe\n0GZz0NDmMpAb2+w0mV1Lo9lO0xllo9mO9VzJly+ARikRoFUSqFERoFUSoFF2fvpp2ssaJf7tZX+N\nEn91R1kxpDzSxQ1t5FaZaGrXaZPZjtFiZ/rIIJaMizir/pdH69l6vMGlv/aHjQCNkgnR/oyJ8I3M\nOr3Fp/IMg8sgrq2t9ZgsgoElPDxcGMKCAaO5ycyX/8qn/GQDkcMNjJs0nOTxUWi0g+Zll+ACyE6Z\nupoWKkoaqShppPREPU31bZ3bdXo1SeMiGT0+irikcFQe9AiWvvkRTdmHMeYepeXoCfQxUQROSCZ1\nza98cna41pJKGrNyaMopwHiwAGPuURym1rPqKXQa/BNG4j86joDRo/BPisM/MRZ97DDUwQa3ymS2\nOzGeYcQ1WxwYLQ6aLXaaza6ya52dFouDFqsDu7N/NotCAj+1yzD2Uys7v+vVSvzUrnX69k+dWoFe\n7dqmVynw07jCO3Rql1GtVyvRKiWfMa6rmi0UN5jb9WqnxerSb/rwAC6NCz6r/lsHqvgw95TrgULj\nOn5/tZIrk0OZEx9yVv2yJjO1Jht+GpcuO3SqVSm8Np32oDSGzxUzLOgbF3scobsR+nRklavVAAAN\n/UlEQVQf7tKl3eZA1c3gFJvVwfGCU8TGh/pEGq3+4uvXptMpY2xso77GRGVpY/vShOWMmFQ/fw2j\nx0cxenwUsQmhKJUDYwD3Rp9Omx3TsWKaDx9n2LIrzzJ8nHY7BY89iz52GPoR0ehjotCNiEYTHjJo\njSTZ6cR0vARjzhGacgpoyT9Oy9GTWKrO7ZBSGQJcxxgbjX7kcPSx0eiGRXKgqpTLFlyJLioMhXZg\nHSCyLGO2O2mxOmhpN5RbrHZM7WWTzYmp3cgzWZ2YrHZabc7OwYKtVgeWPnqkz4UEncZxx6LtYjBr\nz1jfuSg7vktoVQo07eW8vbuZMXMmWqUCjUqBVimhUSpQe8HodjjlTt11LjYHww1aRnUTprS5sI4v\nCutptTlotTlpa/+8IT2K69PPDvP44mgd35YY2x86XA8cOrWCScMDGdtNSrz6VhttNme7Ll16UynO\nrxe3xgxLkrQI+CugAF6VZfmpbuo8CywGTMDNsixnn1nn2LFjPelO0ENyc3N9+g9ysCH06T76osva\n6mZqq1val2bqqltoNpr534fnoz5jdLdaozzvpApDDV+4Nq1WOyajhRajhcaGVhpqTDTUtlJfa6Kx\nzoSjGyMkMEjHsNhgho8MJiYumKiYII/Ed/dGnwq1isCURAJTErvdLtsc+MXF0FZaScOeg5jLqmgr\nr0ap0zJ3/0dn1XdarDRk5aKNDEMbGYrKEIDk4fBASaEgYPQoAkaPYvjyhZ3rbcYWTMdKMB09ScvR\nk5iOnqS1uIK2kkrsxhaaDx2l+dDR09r6t70O6ZG/A6AOMaCNCkcbFYYmLARNWDCa0CDUocHt34NR\nhxhQBxtQGQJQ+ul6ZeBJkuQymtRK+vpW3+Zw0mpz0mp10Gpz0GZzuow363fGW8enuX1bm921rq19\nnbm9bLY7sTpcqdjabO4ZJ1P1zVaiq7oP5Na0G8YaVftnu5Gs6WIwq5UKNO2faoX03fcu69RKCbVC\nQtWljkopoVJIqBWKzu+a9k+VQiJQqyLET41aIaFUSFjtTlRK6TSP78LksG5TzJ3L6ZoU5odaoaDN\n7sTcrt+2dv12x5dH6/nsSC1muxOLXcZid+KUZe6YFsOyCWcPSMyuaCY7O5v58+dfUO8XNIYlSVIA\nzwPzgQogS5KkTbIsF3SpsxhIlGV5tCRJ04C/A2eNSjCZTGeuEvSDpqYmb4swpBD6dB8dunQ6nLS1\n2TC32mgzWTG1WIlPDu82nOGrTwrQ6lSERwWQMnE44VEBBIf5DZh30Jfw5LUpO2VsNgc2qwOrxY65\nzfbd0mrD3GbH3GalzWSjxWimpdllAFst5888EGDQEhLmT2SMgeHtBnBgkHdCDtypT6Vey6jbrz1r\nvcNs6ba+ramZY39+FUtNPdZTdThazaiCAjGMT2LKe8+eXd/YQvVn21AHBaAKDEBlCEAV4Icq0B9t\nRKjbjgNAbQggePI4giePO229LMvY6ptoK62kraSSttJKWksqsFTX4tz3DTp1JJbqOmwNRmwNRloK\ninrUn6RSojIEuo7NEIAq0B+Vvx5lgB8qf3+U/npUAX4o/fUo/fQo9VqUel2XRYtCp3V9arUoNGoU\nOg0KreacWULUSgVBSgVBOveEVDmcLm+1y0h2Gcjm9sk5vlvvKlsc3xlxHdutXdZbHU7aJAsjg3VY\n7E5sDicWh4zV7sTmlLE6ZKwOB/RsjKJHUEigVEidRrKqy6I8Y51S6rqeM8rtiwTbihrYfrIRpfTd\nOkX7/leODuvcVyFJSBJIEnxWUItCcrWrkFx1W20ODh482KPj6MnVMBU4KstyMYAkSe8AS4GCLnWW\nAm8AyLK8R5KkIEmSomRZrj6zsapyYXC4i5Zmi9CnG7no9CnLyLLrFbbTIeOUnTgdMlqdGoXybG9N\nVXkT5lYbDrsTh93pMphsTsZMiELv3+X1qAwtRgv/fGY7tada0GqUaHVqtHoVOr0GtVqBXzeDoOYs\nTD6tbLM6OrMInPMQLnB8veX0XeRumzmt3F7oXCWD3FGSu1aTO/fr8JLI8unfO86H3OUT2TUJQE1V\nM3n7y5GdMrIs43TKyM72zy5lh0NuP59OHE4Zp92J0ynjcLjOrd3uwN5+/uw2J3a7w3UurQ6sVpcB\nbLddeMKG7lCqFAQEagkwaAkM0hMa4U9ouD8h4X6EhPtfdPHcSl334TvayDCmffS3zrLTZsfWaMTR\n2tZtfUdrG/Xb92FvbsFmNGE3tuAwtaKNDmfaRy+eVb/1ZBnZdzzaaSwq9ToUOi1+cTGMfui2s+pb\nG4xUbfoShUaNpFahUKtRaNSogw2EXjoJcHlkNWEu727A2ATaiiuQVEoklZLof6iZfu9PkFSutzeW\n6los1XVY6xux1rkWW30T1vrvPu1GEzZjM842C7b6Rmz1jb3W74WQlEqXcaxVI/1/e/caItdZx3H8\n+zs7u8nmYou0pMVYawhFm2I2L2yqfaEGS2OEUFHwSlARJVRb8G4atIhQqS9ENI1IVVAJCoq92NQ2\nJUGqbUPrZpt7baCYi2x8oTZZuzvOnPn74pzNTjZ7mZ2d7NnZ+X1gmPM8c/bMfx5mz/zPOc95nvwz\nJd0lkp4e1FMiKZVQdwmVSiSlLpSXk+4S6so+29hzcnFdkozVdSWg0XICSUJvkrAkSSBRVq+sXkmW\nuSlRVlYCys7Uj9bviFe5s+sUKonsxawbQAiqIaq1oBpBGlDNH2kNKhH5a1CtQRr5cpo915fTiAvr\nVGpQrWV19fVpLdtOtVajRrZOrTa2rTSFasTF++C6s8QhkQIpE+TuU1wNmHKv3UQ3kUt7Nk+skb3T\nG4BTdeXTZAnyVOucyesuSoYHBwf51Y5nGwzNpvP03n6uDLdnq7g9m3P4hdOX1D29t58rN6wHoFxO\nKZdTyI8zTr3yr7kMb0F44bnDXLvk0Jy9X3dPF909XfT0lPKDmO6xx5LsuXdJN8tet5ileQK8uLd7\n3vaRHe/kyZNFh3BB0l2a8gzv4muu5m0/+mbD21u04mpuvO/LpMMj1EbKpCNlaiNlkkmS89pImfNH\nT1CrVIlKhdr/qtQqFRavuOpCMlxv+PQgBz6zjahUibRG/+BRnn3sIEtWvZH1v9+RfZabxtY/f/QE\nf9mwJU/2EujKksLlb13N+oceoHJuiOq5ISqvDlEd+i9DL73Cie89SH5kmSVHEZSWL+P17+yjNlwm\nHR7JHq+VqZw7z8iZs/nBZEAtsuU0JR1OSYcnn1RkPjpc+QcHnzjSkm115Y+Ff1fF5B7/8NsbWm/a\nG+gkfRC4PSI+m5c/AdwcEXfVrfMocF9EPJOXnwK+GhH99dvaunVr1HeVWLt2LX19fQ0FapcaGBhw\n+7WQ27N13Jat5fZsLbdn67gtW8vtOTsDAwMXdY1YunQpO3funP1oEpJuAe6NiI15+etA1N9EJ+nH\nwL6I+E1ePg68a6JuEmZmZmZm80Ujd6Y8D6yW9CZJPcBHgEfGrfMIsAUuJM//cSJsZmZmZvPdtH2G\nIyKV9HngScaGVjsm6XPZy/GTiNgtaZOkE2RDq33q8oZtZmZmZjZ7czrphpmZmZnZfFLYAJ6SviSp\nJqm1AyV2GEnflvSipAOS/ijp0mlerCGS7pd0TNKApN9Jau38ox1G0ockHZaUSpp4HnabkqSNko5L\n+pukrxUdT7uT9FNJZyUdLDqWdidppaS9ko5IOiTprun/yiYjaZGk/flv+SFJ3yo6pnYnKZHUL2l8\n195LFJIMS1oJ3Ab8vYj3X2Duj4i1EbEOeAzwP1DzngTWREQf8DLwjYLjaXeHgA8Afyo6kHZUN+HR\n7cAa4KOS3lJsVG3v52TtabNXBb4YEWuAdwB3+vvZvIgoA+/Jf8v7gPdJGj+Mrc3M3cDRRlYs6szw\n94GvFPTeC0pEDNUVlwKtmROyA0XEUxEx2n7PASuLjKfdRcRLEfEy0B6Dz84/FyY8iogKMDrhkTUp\nIv4M/LvoOBaCiBiMiIF8eQg4Rja/gDUpIl7LFxeR3dPlfqxNyk+6bgIebGT9OU+GJW0GTkXE3I0g\nv8BJ+o6kk8DHgMZHZ7epfBp4vOggrKNNNOGRkw2bdyRdT3Y2c3+xkbS3/LL+AWAQ2BMRzxcdUxsb\nPena0AHFZZkfU9IeYEV9VR7QdmAbWReJ+tdsClO05z0R8WhEbAe2530KvwDcO/dRtofp2jJf5x6g\nEhG7CgixrTTSnma2cElaBvwWuHvclUqbofzK5Lr8fpWHJN0YEQ1d5rcxkt4PnI2IAUnvpoE887Ik\nwxFx20T1km4CrgdeVDZv50rgr5Jujoh/Xo5YFoLJ2nMCu4DdOBme1HRtKemTZJdWNsxJQG1uBt9N\nm7kzwHV15ZV5ndm8IKlElgj/MiIeLjqehSIizknaB2ykwT6vdpFbgc2SNgG9wHJJv4iILZP9wZx2\nk4iIwxFxTUSsiog3k132W+dEuHmSVtcV7yDrt2VNkLSR7LLK5vxmBmsdXwGauUYmPLKZE/4+tsrP\ngKMR8YOiA2l3kq6SdEW+3Et2Bf14sVG1p4jYFhHXRcQqsv3m3qkSYShwaLVc4J3SbH1X0kFJA8B7\nye6etOb8EFgG7MmHY3mg6IDamaQ7JJ0CbgH+IMl9sGcgIlJgdMKjI8CvI8IHu7MgaRfwDHCDpJOS\nPEFUkyTdCnwc2JAPB9afn1Cw5lwL7Mt/y/cDT0TE7oJj6hiedMPMzMzMOlbRZ4bNzMzMzArjZNjM\nzMzMOpaTYTMzMzPrWE6GzczMzKxjORk2MzMzs47lZNjMzMzMOpaTYTMzMzPrWP8H5Ek0tE/SQYUA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d7ab4c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def logistic(x, beta, alpha=0):\n",
    "    return 1.0 / (1.0 + np.exp(np.dot(beta, x) + alpha))\n",
    "\n",
    "x = np.linspace(-4, 4, 100)\n",
    "\n",
    "plt.plot(x, logistic(x, 1), label=r\"$\\beta = 1$\", ls=\"--\", lw=1)\n",
    "plt.plot(x, logistic(x, 3), label=r\"$\\beta = 3$\", ls=\"--\", lw=1)\n",
    "plt.plot(x, logistic(x, -5), label=r\"$\\beta = -5$\", ls=\"--\", lw=1)\n",
    "\n",
    "plt.plot(x, logistic(x, 1, 1), label=r\"$\\beta = 1, \\alpha = 1$\",\n",
    "         color=\"#348ABD\")\n",
    "plt.plot(x, logistic(x, 3, -2), label=r\"$\\beta = 3, \\alpha = -2$\",\n",
    "         color=\"#A60628\")\n",
    "plt.plot(x, logistic(x, -5, 7), label=r\"$\\beta = -5, \\alpha = 7$\",\n",
    "         color=\"#7A68A6\")\n",
    "\n",
    "plt.title(\"Logistic functon with bias, plotted for several value of $\\\\alpha$ bias parameter\", fontsize=14)\n",
    "plt.legend(loc=\"lower left\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n",
    "\n",
    "Let's start modeling this in PyMC. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal distributions\n",
    "\n",
    "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n",
    "\n",
    "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n",
    "\n",
    "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n",
    "\n",
    "We plot some different density functions below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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A032twBjTBMwBFgMbsWbGN4vIbSJyq11mC/ARsA5YCbxkjNnkWZf6ZDuL+sI5\ni+rTOVSXzqL6dBZ/6rO8tJbCvFJCQ0MYlNm/W9rolxRDVEw4tdWH2Lu7olvaaA3tm0pvIKyT531u\njPmpiKQA3wU6tdrCGLMIOM4jb65H+kngyU7KqSiKoii9DlfYvtSBfYiI7OxXeduICAMG9yVv6wE2\nf1PUbTPmitJb6exMdqiIjDDG7AfWAP4JONgKGifbWTQ+qbOoPp1Ddeksqk9n8Zc+TbNh4xprA5qB\nGc7Exm4Nl2Htb5cR7ZtKb6BTRrYxZj5wyE42ANWOSaQoiqIoSqsUFZZTWVZHdEw4qQP7dGtb/RLd\nXUbKu7UtReltdDpOtjGmwP6/xRjznHMi+Y76ZDuL+sI5i+rTOVSXzqL6dBZ/6XPH5v0ApKT3aXPb\naicQEdIHW7PZm9bu7da23NG+qfQGArkZjaIoiqIoPrLTNrJTBzqzw2N7uFxGtm3QKCOK4gu9wshW\nn2xnUV84Z1F9Oofq0llUn87iD32WHayh9EAN4RGhJKfFd3t7AH0TY4i2XUaKCv3jMqJ9U+kN+LQk\nWUQetKN9eObfb4z5g3NiKYqiKIriyc4t1ix2UmocIQ5to94eIsKAIX3J3XKAzWv3dvtiS8X/fPjh\nh2zZsoXQ0FDS0tK46qqrAiLHhg0bePPNN/nVr37VbtlgkbktfJ3JfqSV/Ie7KkhXUJ9sZ1FfOGdR\nfTqH6tJZVJ/O4g997tx8AICUAf6ZxXbh8sv2l8uI9k3/UVlZyRNPPMH999/PPffcwyuvvEJpaanf\n5XjhhRf4/e9/T1lZWbtlg0Xm9uiQkS0iU0VkKlbovnNdafvvZqCqe8VUFEVRlGOb+rrD7N5VhoiQ\nNsi/MatbXEZq/OcyoviHFStWcPzxx7ekx44dy+eff+53Oe68804uuOCCDpUNFpnbo6PuIq/Y/6OA\nV93yDVAM3OWkUL6iPtnOor5wzqL6dA7VpbOoPp2lu/WZt/UAptmQmBLXbRvQtIZl2CeQt+0gOzbv\n73aXkWDum4vSznCsrhnFXzhWlzv5+fnMmzcPEcEY682D67OIkJWV1WLQFhUVkZDw7SLahIQEcnNz\n/SqDr3SXzE7ToVFqjBkKICLzjDHXda9IiqIoiqJ44grdl5wWF5D2Uwb0IW/bQXK37OecGce1f4LS\nbTQ3NzNz5kwWLFgAwAMPPMDtt9/OyJEjAcjMzOSRR1rz8D2S8vJyIiMjW9Lh4eHU1NR06NzKykoe\neughyspbqlKMAAAgAElEQVTK2LVrFxkZGYSHhzN37lyfZPCVrsjsT3z6KRysBvbatWuZMGFCoMXo\nNWRnZwf1LEJPQ/XpHKpLZ1F9Okt36rOpsZn87QcBGDA4MNubJ6bEERIqlOyvoaaqgdj4yPZP6iTB\n3De7a/bZF1atWsXQoUNb0l988QVPPfVUp+qKi4s7wg+6vr6elJSUDp27bt06nnvuOfbu3Ut2djaz\nZs3qlAy+0hWZ/YnP75tEJBWYBCQBLUubjTGvtnqSoiiKoiidZnd+GQ31jcQnRBHXJyogMoSGhZCU\nEsf+vVXkbT/A2AmDAiKHAkuWLGHKlCkAbNq0iVGjRh1x3N1Vwx1vrhqZmZlHBJAoLS1l/PjxHZLD\n9UPo/fffZ+rUqZ2WwVe6IrM/EZefTIcKi1wKvAZsB8YAG4GxQLYx5txukbADLFmyxOhMtqIoitJb\n+eSDzeR8sYuho5IYOzFwxm3u1gNszNnDiNEpXHpN7/3eLSoqIj09PdBitMp5553HH//4R44//nie\neeYZ4uPjGThwIDNmzPC5rtraWqZPn94S0eXss8/m7bffJjk5mdzcXIYOHdruzqJXXnkl//73vzt1\nLe68/vrrZGdn88ILL7Tk5efnk5GRcYQMbcnsJK31g5ycHKZNm9ZuDE1fQ/j9GvihMeZkoMb+fyvw\ntY/1KIqiKIrSAYwxLbs8pg3yzy6PrZGS3geAgp2lNOvujwGhtLSUwsJCFi5cyOLFi4mMjKSkpISI\niIhO1RcTE8Pdd9/Nk08+yRNPPMFdd93VYqzOnj2bTz/9tM3zq6uriYrq+tuVl19+mddee43ly5fz\n+OOPU1VlBa674YYbWL9+fYdlDiZ8ncmuNMb0sT+XGWP6iUgIUGyMCZgzzFNPPWVuvPHGQDXf6whm\nX7ieiOrTOVSXzqL6dJbu0ufBfVX87dnlREaFcf4lYxA/bULTGkve30Rt9SGuvv1U0od0T5SRQPfN\nYJ7Jfvvtt9m8eTMPP9z9W5Q0NzezfPlyzjrrrG5vKxjx90z2ftsnGyBfRE4HhgOhPtYDgIjMEJEt\nIrJNRH7i5fg5IlIuIjn2X0A3vVEURVEUf5O71dqAJik1LuAGNlhRRuDbjXEU/7Jq1Souuugiv7T1\n3nvvkZWV5Ze2eiO+GtkvA66flk8DS4FvgBd9bdieAf8j8B0s/+7ZInK8l6KfGWMm2H+/9laXxsl2\nFp3ZchbVp3OoLp1F9eks3aXPXTtKAEhM9e8uj63h2m3StcV7d6B9s3Uee+wxv9k906dPJzo62i9t\n9UZ8DeH3uNvneSLyKRBrjNncibYnAduNMbsAROQN4BJgi0e5wP9sVxRFUZQA0Hi4iT27rFBlqbY/\ndKBJTI0nJEQ4uK+a2upDxMR1zhdYCX5iY2MDLUKPxteZ7CMwxhR00sAGGAgUuqV323menC4ia0Vk\ngYiM9laRexgXpeu4VusqzqD6dA7VpbOoPp2lO/RZVFBO4+Fm+vSNIio63PH6O0NYWAiJKdaGOHnb\nu8dlRPum0hvw776svvM1MMQYUysiFwDvAqM8Cy1btozVq1czZMgQwNpec9y4cS2vm1yDVdMdS7tW\n8QaLPD09rfrUtKY13dn0B/MXs2vPXs4ZaS08y1nzFQATTp4U0HTygEwOFFfxwXuLKasZ6fj1uwiU\n/ocNG4aiVFRUtGzXnp2dTUFBAQBZWVlMmzat3fN9ii7iJCJyGvBzY8wMO/1TwLi7pHg5Jw+YaIwp\ndc/XONmKoihKb+Sff1rB3sIKsiZnBmynR29UVdbz6YItREaFMefhaUGxINNJgjm6iOI//B1dxElW\nASNEJENEIoBZwHz3Am6RTBCRSVg/CkpRFEVRlF5Ofd1hindXICFCclpwLHp0ERcfSXRsBA31jRTv\nqQi0OIoSlPhkZItIhIjcKiIvisg89z9fGzbGNAFzgMVYO0e+YYzZLCK3icitdrHvi8gGEVkDPANc\n5a0u9cl2FvWFcxbVp3OoLp1F9eksTuuzMK8UY6Bf/xjCwjsVKbfbEBG3KCPO+2Vr31R6A776ZP8d\nGA+8D+zrauPGmEXAcR55c90+vwC84HmeoiiKovR2CuzQff2SgzPCQ3JaPLt2lJC/7QCTzx8ZaHEU\nJejw1cieAQw1xpR3hzCdReNkO4vGJ3UW1adzqC6dRfXpLE7rc9dOy8hOCZLQfZ4kpsaBwL69VRxq\naCQi0rlYCto3ld6AryOiAIjsDkEURVEURbGoqqin9EANYeEh9E8KzpnsiIgw+vaPobyklt35ZQw7\nLjnQIimdZNGiRVRVVZGXl0diYiI33XST32V46623KC4uJicnhwsvvJDLL7+8zfKLFi2iqKiIhoYG\nBg0axMyZM/0kacfxdeHjPOA9EZktIlPd/7pDuI6iPtnOor5wzqL6dA7VpbOoPp3FSX0W2LPY/RJj\nCQniyB1JqXa87G3O+mVr3/QflZWV3HjjjVx88cX86Ec/4re//S2FhYXtn+ggeXl5lJaWMmfOHJ54\n4gkefPDBlnB53tizZw/bt2/nxhtv5I477uDjjz+mpqbGjxJ3DF+N7DlAKvBb4BW3v784LJeiKIqi\nHLO4XEUSU4JzFttFsr3Ve/72gwGWROksffr0YcmSJURGRiIiNDU14e/wzlu2bOH5558HIDExkWHD\nhrFmzZpWy5eUlLBs2TIOHz4MWDtTRkQE386jPrmLGGOGdpcgXUF9sp1FfeGcRfXpHKpLZ1F9OotT\n+jTGsGtHcPtju+iXHEtIqFB2sNbRLdaDuW8++bNFjtX14G9nOFaXO/n5+cybNw8RaTGYXZ9FhKys\nLC644IKW8ieccAIAK1as4IwzzmjZ3M9fMpx//vm8+eabLecWFxe3uSHQiSeeSHNzM1OnTuX6669n\n6tSphIcHx46o7ji3SkFRFEVRlC5TeqCGmqoGIqPC6NM3OtDitEloqOUzfnBfNbt2HuSE8bqBiz9o\nbm5m5syZLFiwAIAHHniA22+/nZEjrSgvmZmZPPLIIz7V+fbbb/PBBx/w61//usPnVFZW8tBDD1FW\nVsauXbvIyMggPDycuXPn+iRDWFgYo0ePBuCjjz7i5JNPZty4cW2ec++99/LMM8/w6KOP8pvf/KbD\nMvsTn41sERkJzAYGAnuw4ltvc1owX1i7di2646NzZGdnB/UsQk9D9ekcqktnUX06i1P6dM1i90+O\nRSR4/bFdJKfFc3BfNXlbDzhmZAdz3+yu2WdfWLVqFUOHfutc8MUXX/DUU091qc7LL7+c6dOnM2XK\nFN59910GDx7c7jnr1q3jueeeY+/evWRnZzNr1qwuyVBZWcnrr7/On//85zbL7dy5k+XLl/Of//yH\nTz/9lLvuuovRo0czadKkLrXvND4Z2SIyE/gn8AGwCyvG9SoRudYYM7/NkxVFURRFaReXP7ZrUWGw\nk5QaD+ylIFc3ZPYXS5YsYcqUKQBs2rSJUaNGHXHc3VXDHW+uGh9//DFPPfUUixYtIj4+nuTkZN57\n7z3mzJnTrhyuH0Lvv/8+U6ceGQPDFxlcPP/88zz77LPExcVRWFjYqqG/cOFCLrnkEgCmTJnCiy++\nyMqVK3u2kY214PESY8xSV4aITAH+iMeW6P5EfbKdJVhnD3oqqk/nUF06i+rTWZzQZ3NTM4W2sZqS\nntDl+vxBQr9owiNCqa5soLy0lr79Y7pcp/bNtvnkk0+47LLLAFi8eDFnn302ixYtYsYMa5bdF1cN\nEeGss84CLAN4z549jBkzBoDc3FyGDh3a7huVpUuXcscddxyR56vLyssvv8yFF15IQ0MDOTk51NfX\nM3jwYPLz88nIyDhChszMTDZv3tziYlJfX09WVlaH2/IXvkYXGQR87pGXbecriqIoitIFivdUcqih\nkdj4CGJigy9agjckRFpm3XdplJFup7S0lMLCQhYuXMjixYuJjIykpKSk09E1zjvvPAYMGMBLL73E\nI488wgMPPMC5554LwOzZs/n000/bPL+6upqoqKhOte1i5cqVPPTQQ5x33nmccMIJTJ8+nczMTABu\nuOEG1q9ff0T5iy66iAMHDvD0008zd+5cSkpKOOOMM7okQ3fg60z2WuAB4HG3vPvt/IChPtnOEsy+\ncD0R1adzqC6dRfXpLE7os8UfO0g3oGmNpNR49hZWkLvtIONP7XpkCu2brbN06VKuvfZa7rvvPsfq\nvPHGG73mr1ixguXLl7d5blxcHPPmzetS+6eddhoHD3r/gdaakX/77bd3qU1/4OtM9v8AN4tIkYh8\nKSJ7gVuBO9o5T1EURVGUdnBtQpOcFtyh+zxJSrPiZRfmlWKa/Rtj+Vhj1apVXHTRRX5p67333gtK\nN4yegvgacFxEwoDTgHSgCPjSGHO4G2TrMEuWLDE6k60oiqL0ZA4dauSFXy2hqcnwncvHEhHRc6Ls\nGmNYMn8TdbWHuXbOGaQGeXzv9igqKiI9XcMR1tTUEBvbs96qOElr/SAnJ4dp06a1G/qn3ZlsETnb\n7fNU4GwgAjho/z8r0NuqK4qiKEpPZ09+GU1NhoR+0T3KwAZr8VySvfuj+mX3Ho5lA9sJOuIu8qLb\n51da+Qvotupr1wbUJbzXkZ2dHWgRehWqT+dQXTqL6tNZuqrPgp1WVJH+yT3TsHG5jORuO9DlurRv\nKr2Bdo1sY8xYt89DW/lrfe/LNhCRGSKyRUS2ichP2ih3iogcFpHLOtOOoiiKogQ7rvjYyQPiAyxJ\n53BFGNlbUEFjY3OApVGUwOPTwkcRebCV/Pt9bVhEQrDia38HGAPMFpHjWyn3GPBRa3VpnGxn0RXd\nzqL6dA7VpbOoPp2lK/qsrTnE/qJKQkKEpJSeaWRHRYcTnxBFU1MzewvKu1SX9k2lN+BrdJHWooo/\n3Im2JwHbjTG77IWTbwCXeCl3F/AWsL8TbSiKoihK0OPagKZfUgyhYb5+NQcPLpeR/B7ulx0aGkpt\nbW2gxVAChDGGkpISIiMju1RPh1ZWuC1sDBWRcwH3FZXDgKpOtD0QKHRL78YyvN3bTQcuNcacKyKt\n7pWpcbKdReOTOovq0zlUl52nubGR6i25lH+9kYb9JUhoKDkFO5k4bBRhsTH0nTiG+LEjCQnrWQvu\ngomu9M9dOyyjtH9yz9hKvTWSU+PI23qAvG0HOes7o9o/oRUCPdZTUlLYv38/5eVdm5EPFioqKkhI\n6Bk7iAYDxhgSEhKIi+vaeOzo0/QV+38U8Kq7HMA+rNnm7uAZwN1X22u4lGXLlrF69WqGDLEC4Cck\nJDBu3LiWAepaQKHpjqVdOysFizw9Pa361HSg0vV7D/Deb5+mcsN2MneV0lRbx6bmGgBGh8Syu7mG\n3dCSDo2JZtewJOJHj+DiH99F9KC0oLqe3pzetbMJgOKS7dSuKWTCyda8Us6arwB6TLqgaDMFRbmI\njKah/jCrVn/ZKX24COT9SU1NDZr+0dU0wAknnBA08vS0tOtzQUEBAFlZWUybNo328ClOtojMM8Zc\n1+ET2q7rNODnxpgZdvqngDHGPO5WJtf1EUgCaoBbjTHz3evSONmKoijfUvHNFvJfeoPi95ZgGpta\n8iOS+xM9JJ2IxAQw1mwNxtBYVUNtbiGHDpa1lJXQUNIumcbQO2bTZ9xxgbiMY4by0lr+8uRnhEeE\n8p3vjUVC2g2/G9Rkf7ydsoM1XHrtBEackBJocRTFcToaJzvMx3rLReQMY8wXrgwROQO40hhzr491\nrQJGiEgGsBeYBcx2L+AetURE/gq872lgK4qiKBYV32xhy6PPUbbSDmsaIiScPJq+E8cQd8Jwwvu0\n/erzcEUV1dt3Ub5qPRVrN7H3P4vZ+5/FJJ6VxciHbqfvhNF+uIpjD9cuj/2TYnu8gQ2QnBZH2cEa\n8rcdUCNbOabxdXXFbGC1R97XwNW+NmyMaQLmAIuBjcAbxpjNInKbiNzq7ZTW6tI42c7i+bpO6Rqq\nT+dQXXqnqa6Brb96gRUX3EzZyrWEREeROGUSJ/zyHob+z9X0O3W8VwP7q80bjkiHJ8TTL2ssQ++Y\nzejfPkDStNMJiYyg5PPVrLzoVrb+8gWa6hr8dVk9js72z107bCO7h8bH9sS1KU3+9pJO16Fj3VlU\nn4HB15lsw9GGeaiXvI5VZswi4DiPvLmtlL2xM20oiqL0ZkpXrGHDA49Rm1sIIiSeM4kB3zuPsNiY\nLtUbkdiXQbMuJG3mVPZ9uIwDHy8n78V/sv+jzxn77P/SL2ucQ1dwbGOaDQV2ZJHUgb1jYVq/RCtC\nSnlpLdWV9cT1iQq0SIoSEHz1yX4byAN+bIxpdothPdIY871ukrFd1CdbUZRjDdPczPbHXiL3uXkA\nRA5IYdDsC4k/YXi3tFeTt5uCV9+iofggiDDsrmsZ+ZNbkNDQbmnvWGH/3krmPf8FUTHhnHfxaER6\nvrsIwJef7mT/3iq+e8WJjD45PdDiKIqjdNQn29cZ6HuA84C9IvIVUAScT/dFF1EURVE8aKypY+3N\n/2sZ2CEhJH9nMqMevqPbDGyA2KGDOO6RO0m54GwQyH1uHmtu+hmNNXXd1uaxgMtVJDE5ttcY2PBt\nvOw8B7ZYV5Seik9GtjFmNzABuBR4wv4/0c4PGOqT7Szqu+Usqk/nUF1CfdF+vrr0DvZ9uIzQmGgy\n75jFwO/PIDQi3Oe6PH2y2yMkPJz0y6Yz/P4fEhoTxf5Fn/PVpXdQv1cNKehc/3QtekxM7dnxsT1x\n+WXv2lGCL2/MXehYdxbVZ2Dw2ZfaGNNsjFlhjPl/xpiVxpjm7hBMURRFOZKKtZtZccHNVK7fRkRK\nf4bf/0P6nuT/iB/xxw1j5EO3EZHUj8r121hxwU1Urt/qdzl6Ok2NzRTmWWETUwb0CbA0ztKnbxQR\nkWHU1hyi7GBNoMVRlIDgq092BHADcBJwxM9up+Jndwb1yVYUpbdTtno9q2fdR1N1LbEjM8i8bRbh\nCfEBlamxqoa8F/9FzY5dhMZGk/X60/SbdGJAZepJFOaV8ubLXxGfEMWU7x4faHEc5+vl+RQVlDN1\n5glMOD0j0OIoimN0l0/234F7sbZR3+nxpyiKonQD5V9vaDGwE04ezbD7bgi4gQ0QFh9rzaafMo6m\nmjpWz76P8q99c0E5lnG5ivRL6h2h+zxx+WXnbzsYYEkUJTD4amTPAM4wxvzEGPML97/uEK6jqE+2\ns6jvlrOoPp3jWNRlec7GIwzsjFuvJDTcd/9rb/jqk+2NkPAwMm6+gr6TLEN71VX3Up6zyQHpeh6+\n9k/XosekXuaP7SLZvq7CvFKam33zyz4Wx3p3ovoMDL4a2QVAZHcIoiiKohxJec4mVl91L41VNS0G\ndkiYr9sbdD8SEkLGjd8nYeIYmqprWX3VPVR8syXQYgU1DfWN7N1dgQikpPcuf2wXMXGRxMRFcPhQ\nE/v2VARaHEXxO776ZD8AXAE8C+xzP2aM+cRZ0TqO+mQritLbqN6ax8qLb6exooqEk04g47argtLA\ndsc0NpH/0ptUrNlEWEIcp777p24NK9iT2bllP+/My6FvYgxnTR8VaHG6jW++KqRgZwmTzx/Jaedq\nX1B6B93lkz0HSAV+C7zi9vcXnyVUFEVRvFK/7yCrr76fxooq+px4HBm3Br+BDSBhoWTceiV9xh9P\nY0U1q6++n/piDe/njd62lXprJGu8bOUYxqentjFmaHcJ0hXWrl2LzmQ7R3Z2NpMnTw60GL0G1WfH\nqW5oZMO+GgrL69lT2cCeigb2VDbQ0NhMU7OhdPta4oeNJyo8hNS4CFLiIkiNi2BgQiTj0uLI6BdF\nSA/f0KOxppacax6kfs8+YoYOIuOWKwkJ7x4D+6vNG5h0wlhH6wwJCyPz1qvY8dSr1OYW8vU1D3Lq\ne3/q8jbvPQFfxrrLyE5JC/wC1u7EFf977+4KDh9uIjy8YzuE6nPTWVSfgcGnJ7eI/LK1Y8aYR7ou\njqIoxxLNxrD1QC1f765k9e4qthyooa31UYeamjncbDjc0ERVQx07So7cbTAhKowTB8QxfkAcZ2X2\npV+MMwsE/UVzYyNrb/k/Ow52IkPvuJrQqJ63DCYkIpxhc65h2+/mUrVhO2tveZgJ837fI2bj/UFN\nVQMl+6sJDQshMaV3Lnp0ERkZRp9+0VSW1VG0q4yMEUmBFklR/IavPtl/9chKA84B3jHG/MBJwXxB\nfbIVpWdRVnuYRdtKWLi1hOKqQy35IQLpfSJJig2nf3Q4SbFhJMdFEBUWQogIIpaPW32joaK+kYr6\nw5TWNrKv+hCF5Q1UH2pqqStUYNLgBKaP6s+pQxIICwnuGW5jDBt/9Di7X5tvh8a7kehBqYEWq0s0\n7DvItt/NpammjsHXXcrox3/Uq7YO7yyb1hbx4b/XkZwWx2nnjgi0ON3OpjVF7Nyyn6zJmb0yHrhy\n7NFRn2xf3UV+6JknIjOA2b7UoyjKscnG4mre2XiA5fnlNNm/7/tEhjK0XxRDE6MZmRRDZFj7S0Xi\nQiEuMpSBCd/O8hpjKKtrJK+0jq0HaskrrWdFQQUrCipIiApj5glJXDY2mbjI4JxN3fXyv9n92nwk\nIpwht1zZ4w1sgMjUJIbOuYadT71K4bx3iR0+hMzbZgVarIDzrT92757FdpGUFsfOLfvJ367xspVj\nC5+3VffCYuBSB+rpNBon21k0nqazqD5h24FafrZoB/d9sJ3P8sppNjAiMZrLx6Yw58xBzByTzNi0\nuHYN7PWrV7Z6TEToHxPOxEF9uPrkNO6ZPIipI/qSGBNORX0jr60p5po3NvL3r/dSWd/o9CV2iZLs\nr9n6iz8CMOjqmfTxU0QOJ+Jkt0fciAyG3Ph9ALb88o+UZK/u9jYDRUfGujGmZROa5F62lXpr9E+O\nJSREOLivmrraQ+2fgD43nUb1GRh89cke5pEVA1wNFHamcXsW/BksY/8VY8zjHscvBn4FNAOHgfuM\nMcs705aiKP4nv6yOv6/ey/JdVozcyFDhpPR4ThkUT99u9peOiwzjjIy+nD4kgYLyBpblllNQXs8/\n1xTznw37ueLEVK4cl0JEB2bOu5O6wr2svfX/ME1NJE07g8Qze5/rW79TxlFXuJf9Cz9j7S0Pc8bi\nvxI9eECgxQoIpQdqqKqoJyIyjL79owMtjl8ICwulX1IsJfurKcwtZdTYtECLpCh+wVef7GbAAC4/\nlFpgDXCvMeZrnxoWCQG2AdOAImAVMMsYs8WtTIwxptb+PA74tzHmBM+61CdbUYKLusNN/CPHMmab\nDYSHCOPT45icmRBQd42C8nqW7SxnV3k9AAPiI7jzjEFMGpwQEHmaauv58pLbqVy/jbjRwxl+z/VI\nSGCN/u7CNDeT+9w/qNq4nfixIznt/ZcIje55izq7ytfL81m6YAsDhiSQdWZQBuzqFrZtKGbr+mLG\nZQ3iO5c5G9FGUfxNt8TJNsaEGGNC7f8hxpg4Y8xZvhrYNpOA7caYXcaYw8AbwCUe7dW6JeOwZrQV\nRQliVhZUcMvbm3lr/X6MgfED4rj9tHRmHJcYcH/oIX2juHZiGtdMSCUpJpy9VYd4+KNcfv5xLvuq\nOvYa2ymMMWz40WN2JJH+ZNx0Ra81sMHeFfKWK4hI6kfVhu1s/PHj+DLJ01vI22b5JSen9u7QfZ64\n4mXn71C/bOXYod0nuojMcfvs5DLogRzpZrLbzvNs/1IR2Qy8D9zorSL1yXYW9d1ylmNFn2V1h/nl\nf/N4ZHEu+6sPkxoXwTUT0pg5OomEaGdcQ9ryyfaFzH7R3HJqOtNG9CM8VPhiVwW3vr2ZhVtL/Gb4\nFbzyFnvfXkxIVAQZt1xFeB//L4Lzh0+2O2GxMQy98wdIRDhF/28RBa+85df2u5v2xvrhQ00U5pUC\nkDrw2PDHdpHQP4aw8BCqyuupLK9rt/yx8tz0F6rPwNCRaaXfAH+0P+cAfn0yGGPeBd4VkcnAr4Hz\nPcssW7aM1atXM2TIEAASEhIYN25cS+B1V+fSdMfS69evDyp5enr6WNDn1gM1LK5Np6yukbq8bxiT\nGsusc6cREiIthvG4rNMsfQRR+vSMBEL2bGDV7irKE4/n6c8LeHvhEr4/LoUZ06Z0m76qt+Ujv3gJ\ngP3njKO+roxJ9hyDy/B1bRLT29Lrqw5Sdd4EEj/8ki0/f44tYYeIHZERVP25u9KFeaXk7tpAbJ9I\noqJPAiBnzVcATDh5Uq9PJ6bE8dVXK3n37Tquu+l7berLRTDdv56cdhEs8vS0tOtzQUEBAFlZWUyb\nNo32aNcnW0TWAJ8AG4EXgDu9lTPGvNpua0fWexrwc2PMDDv9U6uaIxc/epyzEzjFGFPqnq8+2YoS\nGA41NfPXVUW8vcHaMnlwQiQXjU4isYdtAmOMYUNxDQu3lnCoydAvOowHzh7SLb7ah8oq+eL8G6jf\nXUzi2acw+NpL2j+pF7L7Xx9wcOlKogcP4Iwlfw/ITL6/+eT9zeSs2MWw45IYM2FQoMXxO3nbDrDh\n6z2MHJPKJT84OdDiKEqncdIn+yogASsWdjhwrZe/azoh4ypghIhkiEgEMAuY715ARIa7fZ4ARHga\n2IqiBIY9FfXcM38bb284QIjA5IwErp2Y1uMMbLDC/40bEMetpw5kcEIkZXWNPPxRLq98tYemtrag\n9BFjDBvu/TX1u4uJzhhI+qzvOlZ3TyP9iu8QPXgAdYV72fDA744J/+y87daP0ZSBgVloG2iSbD/0\nwtzSY+J+K0q7RrYxZpsx5mZjzPnAMmPMuV7+pvrasDGmCZiDFWd7I/CGMWaziNwmIrfaxS4XkQ0i\nkgM8D1zprS71yXYW9d1ylt6ozy8LKpjz3jZ2ltTRLzqMq09KY8qIfoR0825+Tvlkt0bf6DCunZjG\nucP7IsCb6/bz0KIdlNcddqT+/D+/zv6PsgmNjSbj5u8TGh7YHyT+9sl2JyQ8nMzbriIkMoJ97y9l\n92vvBUwWp2hrrJeX1lJ2sJbw8FASj5FNaDyJ6xNJVHQ49XWHOVBc1WbZ3vjcDCSqz8Dga3SR9h1Q\nfLVztYsAACAASURBVKtvkTHmOGPMSGPMY3beXGPMS/bn3xtjxhpjJhhjzjTGrHCyfUVRfKPZGF5b\nU8wji3OpOdTEyKRobjxlAJn9owItmmOEiHBmZl9+MCGVmPAQ1hZV8z/vbmXL/pou1Vu2ej3bfvMn\nAAbOvoiotGQnxO3RRKYmtbjLbP7fp6natCPAEnUfrqgiiSnWxizHIiJCygBrNnvnpv0BlkZRup9e\nES/qpJNOCrQIvQqXw7/iDL1FnzWHmvjFf/OY9/VeAM7KTODKE1OIDg/1mwyuxYv+ILNfNDdPSie9\nTwQHaw5z/wfbWbytpFN1HS6v5JvbHsE0NpF47qn0P3W8w9J2DtdixEDS79Tx9J88keZDh1lz8//S\nWNN+5Ilgpa2xnr/NchVJPMZC93mSYkdV2b5pX5vlestzM1hQfQaGXmFkK4rSveyrOsS987exYlcF\nUWEhXD42mXOG90O62T0k0PSJCuP6iQOYODCOxmbDk58V8NdVRTT74E9qjGHDA49Rv2cfMZkDSb9i\nRjdK3DMZNOtCIgckU5tbyKaHngy0OI7T2NhMQa61nCht0LHpj+0iOTWekBBh/94qaqv9G5teUfxN\nrzCy1SfbWdR3y1l6uj63Hqjh7vlb2VVeT1JMONdNSOX41NiAyNLdPtneCA0RLjg+iQuO648Ar3+z\nj998kk9DY8f2xtr9z/nsW/ApIdGRDL7x8oD7YbsTSJ9sd0IiI8i8bRYSHkbRvxey598LAy1Sp2ht\nrO/JL+PwoSbiE6KIiY3ws1TBRVh4KIkplk967rbWXUZ6+nMz2FB9BgafjGwReVpE1DdDUY4RlueX\n8+AH2ymraySjbxTXTUgjJf7Y2wobYOKgPsw6KZWIUOHzvHIeXLCd0tq2F0RWb81j8/89A8DAKy4g\nekCKP0TtkUQPTGXQ7IsA2PiT31O9PT+wAjmIK6pIYuqxueDRE9dGPNs3ql+20rvxdSY7FPjIjvjx\nExEJikCf6pPtLOq75Sw9VZ/vbNjPL/+bR0OTYUxqLLNPSiEm0n/+197wp0+2N4YnRvPDrAEkRIWy\n9UAt98zfxp6Keq9lm+oaWHv7IzTXNdB30okknpXlZ2nbJxh8st3pP3ki/SadSHNdA2tveZimuoZA\ni+QTrY31fHvRY8qAY2uXx9ZISbf0ULCjhKYm72+EeupzM1hRfQYGX6OL3A2kAz8FTgI2i8h/ReQ6\nEdGf6IrSCzDG8Jev9vCnlXswwOTMBC4dk0RYaK/wLusyyXER3HhKOgPiI9hXfYh75m9j64GjI49s\n/eUfqd68k8jUJAb9YGYAJO15iAiDrr2EiJT+VG/JZcujzwZapC5TVVHPwX3VhIaFkKwz2QDExkUS\n1yeKw4eb2JNfFmhxFKXb8Plb0xjTZIz5wBgzGzgNSAb+BhSLyF9EZKDDMraL+mQ7i/puOUtP0mdT\ns+EPnxfw73X7CRG4YFQiU4JogWMgfLK9ERsRyrUT0hjWP4rKhiZ+tGAHq3dXthzft3AZBX99GwkL\nY/AN3yMsJjqA0rZOsPhkuxMaFWn5Z4eFUjjvXYrf/yTQInUYb2N952bLJSIxJZYQ/aHaQmp621FG\netJzsyeg+gwMPo94EekjIjeJyFLgM+BL4CzgBKAa6JkrVhTlGKehsZlf/jePj7aVEh4iXDommYmD\nj+1wY20RERbCVeNTGZcWS31jM//30U6W7Cilbs8+Ntz3WwBSLzqXuBEZAZa05xEzJJ3071tRWDbc\n/zvqCvcGWKLOs2OzZUSmpKmriDsuv+ydmw8EWBJF6T7El61NReQt4DtYxvU84F1jTIPb8RCgwhjj\n12/mJUuWmAkTJvizSUXpVdQcauL/Fu9kQ3EN0eEhXDYmhaGJvWeDme7EGMMnO8pYUVCJNDdzz1t/\nJmTdRuLHjGDYPdcHzVuAnoYxhrwX/knlN1vomzWWSe++SEhYWKDF8on6usO8+JtPaDaG6ZeOITIq\neCLLBJrmZsPi/2zg8OEmbrr/LPolBSZikaJ0hpycHKZNm9buw93XmeyvgJHGmAuNMW+6DGwRuR/A\nGNMMpPosraIoAaOyvpEff7idDcU19IkMZfZJqWpg+4CIMG1kf6aN6MekZR8Rsm4jTX3iGXz999TA\n7gIiwpDrv0dYQjzlqzew86m/Blokn8ndeoDmZkP/pFg1sD0ICRFS0u3dHzdrlBGld+Krkf2wMabY\nW77rgzGmtmsi+Y76ZDuL+m45SzDrs7T2MA8u2M72g3X0iw7jByenkt4neEP0BYtPtjcmle/mjE8W\nYET4z+X/v737jo/jLhM//nlmu7qsZrl3O7Ed24ljHBJSMBdSIAlJACeBQOgttByQgws1B4QS2gF3\n3AG/wHEHBEIKhJCeEAfHdty7bNmWbdnqklW3zfP7Y1eybMu2JK+0Wvl5v17z0s7s7Myj0e7Oo+88\n8/2+m8d8ZQzgQmFajMSa7N68udlMfv9bQWD39/8fDSvWpjukUzr+s16xJVkqYr2K9Km7l5GdfdRl\nj+TvzUxkxzM9+nXtTURe372+iFwB9G6emQa0pjowY8zQqmuP8LnHd3GgJUxRlo9bFpZSELLWtsHQ\nllYiX/42okrDxa/lwLTZ7G8XulS4NacTa9AevNzZ0yi75nJq/vI8Gz/yJS5+7n/wjxn5oyZGo3H2\nJLvuGz+pIM3RjEyl5XkgcGh/C+GuGIFgZpUDGXM6/arJFpE9yYeTgKpeTylwGPimqj6a+vD6x2qy\njRmYQ0fCfPbxXdS0RSjN8XHLgjJy7QQ3KKpK5O57ib+4EplQjuf976DCk8MjWoQrwmWhMHfkduBY\noj1oGo9T8e2f07G7ipIrL+b8B7414ktxdm2r5eFfryW/MMSlV81Odzgj1oqnK2isa+dNyxcw57zy\ndIdjTL+ktCZbVaeq6lTgN92Pk9M0VX1tOhNsY8zAVDV3cdefK6hpi1Ce6+e2RZZgn4nYg48Rf3El\nhIJ4bnozjtfLbOniZqnHqy4vdAb4jyPZxEZ46chIJh4PU97/VpxQgLonV1D1iz+mO6TT2pUsgSgp\ntx56TmXshMRViW3rq9MciTGpN9DBaG4fqkDOhNVkp5bVbqXWSDqelQ2d/POfK6jviDIhP8Bti8rI\n9mdOgj3SarLd7RVEf/RzADzXvgGntKjnuWkS5m1Sj19dVnb5+VFLNpERlmiP9Jrs3vxFhUx611sA\n2P6VH3FkS0WaIzpR92fdjbs9N/ONm1SYzpBGvHETE6U0eysaiIRjPctH0vfmaGDHMz1Om2SLyKW9\nHr/+ZNNgdi4iV4nIdhHZKSKf6+P5W0VkQ3J6SUTmD2Y/xhjYUdfOZx6voLkrxuTCILcuLCXoS+8w\n6ZlM2zsI/+t9EIvhXLgQz6ITv54mSYRbpI6gxlkX9nN/cw7hEZZoZ5KCC+ZRdOliNBJl/QfuIdbe\nme6Q+nRgXxOdHVGycwPkFVhPPacSyvZTWJxNPO5Sud36zDajy2lrskVks6rOSz7ec5LVVFWnDWjH\niT61dwLLgGpgNbBcVbf3WmcpsE1VW0TkKuDLqrr0+G1ZTbYxp7b5cBv/+rfddERdpo8JcfP8Enxe\nG31usFSVyBe/RfzpF5FxZXje906cwMlvGq1VL7/VEjrEw0xfjLsKWsmywz8objjCjn/7KeFDdYy/\n9c3Mv/9f0h3SCZ59bBtr/7GPKbOKmX/BhHSHM+JV7qhjy9qDTJ1VzE3vXpzucIw5rZTVZHcn2MnH\nU08yDSjBTloCVKjqPlWNAr8Frj9u3ytVtSU5uxIY9iHbjcl0aw8e4V+eSCTYs0uyeNuCUkuwz1D8\n0b8Rf/pFCATw3PimUybYAKUS4x1SR67GqIh6ua8pl1Z3ZN+4N1I5AT9TPvB2xOvh4P8+xqGHn053\nSMdQVSqSozyWTxz5vaCMBN3Had/uBsJdsdOsbUzmGNCZVkSuEJGpycdjReQBEfmFiIwdxL7HA/t7\nzR/g1En0+zjJkO1Wk51aVruVWuk8niurWrjnyUrCMZe5ZdncNL8ETwZ3czESarLdXXuJ3P+fAHiu\nvgKnvLRfrxsjMW6TOvI1xp6Yl2805tIcT+/fIpNqsnsLTRjL+LddA8Dmu75Be+X+07xieLz00kvU\nVB+htbmLQMhLUUlOukPKCKEsP2NKsnHjyu7kPyh2HkotO57pMdA7nn5CYlh1gPuTP2PAz4DrUhXU\n8ZJ9c98BXNLX8y+88AJr1qxh0qRJAOTn5zN//nwuuSSxeveby+b7N79p06YRFU+mz6freLrj5vKN\n5/bStGs9M4pC3PD6KxGRnkR1/uJE5ZXN939eO7tY9+nPoF1NzD3/NXguXMTm3dsAmDf9HIBTzhdI\nnMW7X+AZzefAjMV8vSmXK2v+QZ6jLDkncdGwO/G1+VPPX3j5Etp27OHl1a+w6+0f5AN//xOeYCDt\nn/c//v5x9h08xCWXXIKIsHbdKgDOX7QEwOZPMj9u0lQa69p56MG/0tg+h27p/nuOlvluIyWeTJvv\nflxVlejFevHixSxbtozT6Vc/2T0rixxR1TwR8QI1wGQgAlSranG/N0RPvfWXVfWq5PzdJGq77ztu\nvfOAPwJXqeruvrZlNdnGHOupiga++2IVrsLi8bm8cfaYEd+vcCYI3/s94n95GiktxvPB23GCgxsd\ns10dfkcxtfgpduLcXdhGqddNcbSjX7yjix33/oRIXSMT3nk98759wv3zw8p1lf/69gu0tnTxmsun\n2UiPA9DVGeWpR7bgiPCRL7yeoA2MZUawlPaT3csRESkDLgO2qmpbcvlgPg2rgRkiMllE/MBy4Jj+\ntkVkEokE+50nS7CNMcf687Z6vv1CIsG+aFKeJdgpEnv8GeJ/eRp8Pjw3XTvoBBsgW1xupY5ywtS7\nHu5tyqU6ZnXyA+XJCjLlQ8sRr4cDv36E6oeeTGs8+ysbaW3pIivHT8lY6x97IIIhH0UlObiu9vQx\nbkymG+i3+o9IJMe/AX6cXHYxsP2krzgJVY0DHwOeBLYAv1XVbSLyQRH5QHK1e4AxwE9EZJ2IrOpr\nW1aTnVpWu5Vaw3k8/7Cplh+uSNSnXjq1gGUzR1eCna6abHfvfiLf+QkAnjdejjNh3BlvMyjKcuqZ\nSBfNrsO/NeZSFR3eLhUztSa7t6xJ4xi//FoANt/1Tdoq9qYtlgd/+2cAyifkj6rP3XAZlxx+fuv6\najsPpZgdz/QY6GA09wFvAC5W1d8mFx8A3juYnavqE6o6W1Vnquo3k8v+U1V/lnz8flUtUtXzVXWR\nqi4ZzH6MGe1Uld+sO8zPXjkIwLIZhVw6rSDNUY0O2t5B+PNfh84uZN4cnKUXpGzbAVHeRgNT6KRV\nHb7elMPuYU60R4OiSy+kYMl5uJ1drHvP54m1dwx7DJFwjAN7mgCYOL3oNGubvpRPLACB/ZVNhLui\n6Q7HmDM20N5F/MDlwF0i8isR+RWJ1ubPDkFs/bZw4cJ07n7U6S74N6kx1MdTVfnFmkM88OohBHjj\nrDFcNHl0dh3WfTPicFFVIv/2fXRPVaIO+4arU95C6RPlZhqYSQcd6nBfUw7bI8MzCmf3zYSZTkSY\n+M7rCYwtpr1iL5s/+XUGcr9RKuzcUsOEsjkUFmeRm2cD0AxGIOiluDQHVaUkf0a6wxlV7LyeHgMt\nF3kA+CTQCuw+bjLGDLO4q/xgxX5+t6EGR+CaOUVcONFutkqV2G8eIv7cCggG8Lz1OpzQ0CRPXoEb\naOQc2ulSh2835bApnDnD3Y8EnmCAqR+5DSfo5/Bjz7L3p/83rPvfujZxFal8ol1BOhPjJyeGod+4\namR0y2jMmRhokn0V8FpV/ZyqfqX3NBTB9ZfVZKeW1W6l1lAdz0jc5evP7eXx7Q34HOH6c4tZNH50\n32w1nDXZ8dXrif70/wHgue6NOOPKhnR/HoE308R5tBFF+F5zDmu7hraHhdFQk91bsLyESe+5GYAd\n9/6Yhr+vGZb9HmnupGpPI1WHtzFx6phh2edoNW5SAV6vwyurVlJf05rucEYNO6+nx0CT7Cpg8LfU\nG2NSoiMS556/7ebve5oJeh1uml/C3LE28EWquIdrCX/xPnBdnIuX4Fkwd1j26whcTTMX0EoM4Yct\n2awc4kR7tClYdC5l11wGrrL+/f9K5/5DQ77PreurQaFwTBb+gF2BOBNen4fxUxKt2etXWmu2yWwD\nTbJ/BTwiIreIyOt7T0MRXH9ZTXZqWe1WaqX6eLZ0xfjs47tYV91Gjt/D8gVlzCjOSuk+RqrhqMnW\nzi7Cd98LzUeQGVPwXHXFkO+zNxF4Ay0s5Qguwk9bsnm6Y2jaNkZLTfbxxl6/jNy5M4k2H2HtHXcT\n7+gasn2pKluSpSKXX3HpkO3nbDJ5ehGTx5/L1vUHiUbi6Q5nVLDzenoMNMn+GFAGfB34ea/pv1Mc\nlzGmD7VtET712E521ndQGPJy66IyJhTYxaVUUdcl8tXvojt2Q1EhnpuvQ5zh779aBC7jCJfRgiL8\nqjWLh9qCDPO9fBlLHIfJ738r/uJCWjdXsPHjX0XdoRns5/CBFprqOwgEvYydYPXYqZA/JouCMVlE\nwnF2bBr6KxHGDJWBduE39STTtKEKsD+sJju1rHYrtVJ1PKuauvjkYzs50BKmNMfHbQvLKM3xp2Tb\nmWKoa7KjP/s18edfhlAQ7/IbcHKzh3R/pyICF0krV9OIqPJwe4gHWrNwU5hoj7aa7N682VlMu/Od\nOMEANX9+nopv/deQ7Gfzq4lW7LET8lm/YfWQ7ONs1BZLDF+97h9VaY5kdLDzenrYEGPGZIDtte18\n+s87qW+PMiE/wK0LyyjIslrdVIr99VliD/weHAfPjdfijBub7pAAWCAdvEUa8KjybGeAH7dkE7EW\n7X4JjitlygeXgwiV33+Agw/+NaXb7+qMsmVdNQATp9kNj6lUXJaD1+dQU32EusN2A6TJTANOskXk\nn0TkFyLyWHJ+sdVkjy5Wu5VaZ3o8V+8/wmcf38WRcJxpY0LcsrCUnLP05qqhqsmOb9hK5Bs/AMBz\n5eV4zp01JPsZrFnSxduljoC6rA77ua8pl1b3zPvrHq012b3lzZvJ+FuSI0J++hs0rdqYsm1vWLWf\nWDROcVkOhUXZnL/IxktLlQsXL2XClMQ/LutXWmv2mbLzenoMdDCaO4GfAjuB7js8OoF7UxyXMQb4\n87Z67nlyN10xl3NLs3jbeSUEvDYiYCq5VQcJ3/01iMZwLliA53WvSXdIfZokEW6TWnI1RkXUy1cb\nc6mJ2cXI/ii5YinFVyxFozHWvuuztO85cMbbjMdc1v1jHwBTZhaf8fbMiSYlR87cur6aSCSW5miM\nGbiBfkN/EnhDcgj07rtItgOzUxrVAFlNdmpZ7VZqDeZ4uqr87JWD/HDFflyF10zM4y3zSvB6zu6k\nKtU12W5dA+FP/GtPTyLOdW9M6fZTrVRi3C61lBKhJu7hK4257IoM/p+u0VyTfbzxb7860eNI0xHW\nvO0TdNXUn9H2tm86RNuRMDn5QcZOSIywunbdqlSEakgcy/zCEAVFWUQjcXZsPJzukDKandfTY6Bn\n7Fygu+PK7qpAHxBJWUTGnOXCMZd7n9nLHzbV4khimPR/mjUm5cN5n+20rZ3wp7+EHq5FxpfjueVG\nnAy4SpArLrdRx1Q6aVOHbzTl8or1pX1a4vEw5UPLCU0eR+f+Q7x6y6eJHmkb1LZUlVdf2gvAlOn2\n2RxKk2ckWrPXvLQXte51TIYZaJL9InD3ccs+DjyXmnAGx2qyU8tqt1JrIMezrj3CXX+u4KW9iUFm\nbp5fasOk95KqmmwNRwh/9mvorj1QPAbPO27CCWZOV4gBUW6mgQXJ0SF/3JLDH9uCA+555Gyoye7N\nEwww/RPvIlBaROvWXay9/TPEu8ID3s7+ykZqD7USCHqZmCxpAKwmO4W6j+X4SYUEgl4aatuo3F6X\n5qgyl53X02OgSfadwFtEZC+QKyI7gLcBn051YMacbbbUtPGxh3cc0wf2rJKzY5CZ4aSxOJEvfxt3\n3SbIy8X7jptx8jJvOHqPwFU0s4xmRJVH2kP8e0s2XUPTHfSo4c3NZvqn3403P5emlRvY8KEv4sYG\nVu+7JtmKPWHqGLwZcPUjk3m8DtPPKQXgpacqrDXbZJSB9pN9CLiQRGJ9K/AuYImqprVYymqyU8tq\nt1KrP8fziR0NfPYvu2jqjDG5IMjtF4xlXF7mtKwOlzOtydZYnMhXv3u0L+zbbsQpKTr9C0coEbhQ\n2nir1BNQlzVhP19ryqUu3r+v9rOpJrs3f1Eh0z/1bpxQkNon/s6mj9+Lxvs3smBDbRuVO+pwPMK0\nWSXHPGc12anT+1hOnlFMIOil7nArlTusNXsw7LyeHqf9JhaRr/aegK8AbwLmA9cAX04uHzARuUpE\ntovIThH5XB/PzxaRl0WkS0SstdyMOtG4y49f3s/9f68i6iqLxuVwy8JScs/SLvqGksbjRL52P/Gn\nXoBgAM8tN+BMGJfusFJimoS5XWop1Cj7Y16+2JDLhrC9h04lNL6M6R+/HSfg59BDT7Lx41/rV6L9\n6oq9AIybVEDQ+qofFl6vw/Q5idbsFdaabTKInO7NKiK/7DUbBG4CVgP7gEnAEuCPqnrLgHYs4pDo\nCnAZUJ3c5nJV3d5rnWJgMnAD0KSq9/e1rWeeeUbPP//8gezemLSraY1w77N72FHXgUfg9TPG8JpJ\nVn89FHoS7L89DwE/nltvxDNjarrDSrkuFR5jDLsJISjXZ3dxQ3YXjt2Xd1JtFXup/MGvcMMRym+6\nkvN+eA/i6bsEpLmxg19+7+/E48qlV80iv9DKuYZLLBbnmUe3EQnHuPFdFzBtdsnpX2TMEFm7di3L\nli077TfraVuyVfWO7gkQ4BZVvVhVb1XVS4Dlg4xxCVChqvtUNQr8Frj+uH3Xq+qrgHWQaUaVV6pa\n+MjD29lR10F+0MMtC8dagj1ENB4ncu/3jybYt7xlVCbYAMHkDZGX0gIKD7eH+E5zTkoGrhmtcmZO\nYdonki3afzx1i/aLT+wkHlfGTS6wBHuYeb2entpsa802mWKgNz5eDTx83LJHSZSNDNR4jnYHCHAg\nuWzArCY7tax2K7V6H8+Yq/x8dTX3PFlJa3IExzsWlzNlTDCNEWaOgdZkazhC5J77iD/xbCLBXv4W\nPDOnDVF0I4MIvFZaebvUE9I4myM+vtCQx9bIieUjZ2tN9vGOT7Q3fPjLuOFje6Y9uK+JnZsP4/E4\nzJk/ts/tWE126vR1LKfMLMIf8FBTfYR9uxrSEFXmsvN6egy0aG8X8FHgh72WfRjYnbKIBuGFF15g\nzZo1TJo0CYD8/Hzmz5/f02VN95vL5vs3v2nTphEVT6bPdx/PyfMWc9/z+1jzyssIcPWyy7hsWgGb\nX30FONo9XXciafNnNj9vznzCn/0am19dCX4/85e/Hc+saWzevS3x/PRzAEb1/B3U8vPdB6jCx33T\nF3BNVphJ+1fjkaPd93Un2jY/j2mfuJ3H7v8JWx9+lEhDE4t++U1e2bgedZV9mxOnyy4OsGNXV08X\nc93JoM2ndr5b7+e9Xg8Rp5p9Bxv4+5N5TJ5RxIoVK4CR830/Uue7jZR4Mm2++3FVVRUAixcvZtmy\nZZzOaWuyj1lZZBHwJxLJ+UESLc8x4EZVXdvvDSW2tRT4sqpelZy/G1BVva+Pdb8EtFpNtslEqspf\ntjfwnysPEI4r+UEv18wew/Riu9w8VLS+ka5PfxGt2AN5OXhvvQln4ui4yXGgXIWXyWWF5qEiTPHG\n+HB+O+Ve6+uvLx1Vh6j8wQPEjrSRe+4MLvi/+6k8FOHx328kGPJy+TVz8PntptJ0iUXjPPNYojb7\njTfNY/4FE9IdkjkLpawmuzdVXQfMBG4B7ifRjd/MgSbYSauBGSIyWUT8JGq7Hz3F+lZUaDJOQ3uU\nLz5ZyQ9X7CccV84tzeK9S8otwR5C7r4DdH3gnxMJdvEYvHfcetYm2ACOwCXSym1SR57G2Bvzck9D\nHk+0BwY8eM3ZIGtSOTPv/gD+0jG0bt3Fius+zAt/2QrAjHPLLMFOM6/Pw9zzE5/n5/+ynfbWgQ8m\nZMxwGWhNNqoaVdW/q+rvVPXF5E2LA6aqceBjwJPAFuC3qrpNRD4oIh8AEJEyEdkPfAr4gohUiUjO\n8duymuzUstqtM6eqPL69nvf9cRtPPf8iQa/Dm+YUceP8UrJ8NnjFYJ2uJju+YhVd7/0UeqgGGT8W\n73tvxSnN3H6wU2mCRHiP1DCXdiII/9uWxZ2rKzkYG/BpYNQLlIxh1t0fJGvKeA4WTKW9PUaOX5ky\no/iUr7Oa7NQ51bEcP7mQkrG5hLtiPPvnbcMYVeay83p6pPVfclV9Aph93LL/7PW4Bpg43HEZcyYO\ntoT5/ktVbDjUBsD43AC3X1hOofWpO2RUldgDvyP6s/8BVWTODDw3vxknZDeU9hYU5c00MUc7+ZsW\ncDDm4Z6GPG7I6eKarC68dr2whzc3m7I738uajYl2pOJH/4eW8G7yb7kJETtQ6SQinHfhBJ57fDs7\nNh1m7vl11qWfGZEGVJM9UllNthkJwjGXBzfV8tv1h4nElWy/wxXTClkwLsdOykNIOzqJ3Ps94s+t\nABE8l16E84ZLEesc+pS6VHiWfDaSuDhY7olze24HcwPWYyqA6ypPbolR36YUtNcx4Xc/BSDrkqWU\nfOZOnKxQmiM0u7fVsnV9Nbn5Ae745Ovw2yBeZpgMSU22MeZEqspLe5t53x+28atXDxFJ1l6/f8k4\nFo7PtQR7CLnbK+i645OJBDsYwPO26/BceZkl2P0QFOUaaebt1FGoUQ7FPdzXnMu/N2fTELfjt2F/\nnPo2JeCF2fPLyH7XbRAI0PHSSqo/9lnCuyrTHeJZb+rsEvIKQ7S2hFnxdEW6wzHmBKMiybaa7NSy\n2q3+29PYyd1/3cVXn95DTVuE0mwfyxeUceP8UnKSrSoD7dvZnFz3sdR4nOgDv6frfXehVQeQSHQ+\nFAAAFjtJREFU0mK8770Nz3nnpjnCzLJ59zamSpj3Sg2X0YxXXVaF/XyuPp+H2oJ0nqUdkFQ3u2yp\ndhFgZqmD3+vgP2c2eR/7IE5JCdH9B6m+83M0/98fjxm4xmqyU6c/x9JxhAVLEhWla1/ex75d9UMd\nVsay83p6jIok25jhVn0kzDef28uHHtrOuuo2Ql6HZTMKed+SccwotsvIQ8k9VEP4o/9C9D8egHgc\n58KFeD78LpxxZekOLWN5BS6SNt4vNcymgwjCw+0h/rk+nyc7AkQzv6qw3zojysu7EiUzE8YIhTlH\nT5OekmLy7vwggaVLIBan6Re/4dBd9xA9dDhd4Z71CsZkMXNuGarwyG/W0VDblu6QjOlhNdnGDEB9\ne4TfrDvMEzsaiCt4HDhvbA6XTSvoabk2Q0NjMWK/e4Toz/8XOrsgLwfPtVfimTf79C82A7Jf/Tyv\n+RyUAADFTpwbcrp4bTAyqm+OVFWe2RbjcIuSH4L5EzwnLfeK7qyg/cE/oa1tSChI4e3LybvhGsRr\n3wPDTVVZ89JeDh9oIb8wxDs+ehGhLH+6wzKjWH9rsi3JNqYfDrR08eDGWp6uaCTqKgLMLcvm0mkF\njLFeQ4ZcfN1mIt/5CVq5DwA5dxaeN78RJ++EHj1NiqjCLoI8r/k0SOI9XuTEuTY7zKWhMP5Rlmyr\nKqv2xKmocfF5YMEkh5Dv1Bd73fYOOv70KNHNiX60fVMmUvSxDxBaMHc4Qja9xGJxVjy9iyNNnYyf\nUsjb3nMhHq9drDdD46y68dFqslPLareO2lHXztee2cN7H9zGX3c0EHOV2SVZvOfCcm6YV9KvBNtq\nsgfPPVxL+CvfJfyRz6GV+9ia7eC55S34brvJEuwU6B6CvS8iMFO6eK/U8CYaGaNRGlwPv2rN4q76\nfB5rD9Lqjo5MW1VZnUywHYGZZadPsAGc7Cxy3rGcnHffhlNYwIbK7Rz+53uo/eb3idVaffCZGGh9\nu9frYcmlUwkEvRzc28RTj2xhNDQipoqd19PDrmsZc5xwzOWFyiYe21bPjroOIFEWMrc0m6WT8ynN\nscuQQ00bGok+8HtiD/8VojHwevFctBjPlGI8c+akO7yziiMwjw7m0sFOgrysedS4fh5sC/GntiBL\ngxH+KSvMVF/89BsbgboT7J3JBHtOuUNRzsDan3xzZpM3fRr+h34Hmyppf+ZF2l98mbxrryR/+Y14\ni8YMUfSmt1CWnyWXTmPFMxVsfvUgPp+HK950Do71NmTSxMpFjEna09jJkzsbeLKikdZwImEIeR3m\njs3mokl55IesLGSoaUMj0d89Quz3j0E4DCLI3Nl4Xn8JTpkNNjESqMJeAqzWHCoJJpq8gWneGK8L\nhVkajJLtZMZ5RVVZszfOjsOJBHv2WIfi3DO7wBtvaKTziaeIbtoCgAT85F13NflvvR5PYUEqwjan\ncfhAC2tW7EVdZfqcEq5dvgC/39oUTepYTbYx/VDfHuHZ3U08u6uRysaunuXluX7OK89hQXk2fq8N\ngz7U3B27if7+EeJPvZBouYbEqI2XX4wzcVyaozMn06Qe1pLNRs0hLInk1IuyKBDlklCEef4ovhHa\niBiJKasq4+xtcBGBOWUOxXmpq6CMH66h82/PEN22PbHA5yXn8teRd+O1BGZMS9l+TN8aattY/eIe\notE4ZePyuPFdF5CdG0h3WGaUOKuS7O9+97v6nve8J91hjBovvfQSl1xySbrDGDLVR8K8vLeZl/e1\nsKWmne5PQMjrMKskiwXl2UwqTF03fJvWrGT+4qUp295ooV1dxF9YSezhv+Ku35xYKILMno5z8Wvw\nTJt0wms2797GvOnnDHOko1eqjmdUhZ0E2ajZ7CPQ07odEmVhIMLiQJTzAlECIyThrmt1WVERoy0M\nnmQNdkkKEuyNu7Zw3oxjb3qMHaim8+nniO3YQfeXTWDeOeRddzVZF12IE7TEry9r163i/EVLzmgb\nbUe6WPl8JZ3tEfIKglx/2yLKxuenKMLMMtrP68Otv0m2XT8xo14k5rKlpp21B4/wyv4j7G062mLt\nEZheFOLc0mzmlGXjtdq9IaXxOO7aTcSeeJb48y9DR2fiiUAAZ8G5OBddiFNalN4gzYD5RJlLJ3Ol\nkyPqYQshtmoWdfj5R1eAf3QF8KOc448xPxBlvj/KWI/LcA+G6qqy5aDLxv1xFMgOwKwyh5zg0PUB\n4J0wjtx330a8oZHwyysJr1lHePM26jZvQ7JCZF+ylJxllxFcMBfx2FWzVMrJC/K6K2ey6oU9NDd2\n8D8/+QeLLprMxW+YSSBo6Y8ZeqOiJdvKRUxvkZjLzvoOttS0s766lc2H2wjHj77PA15hWmGI6cUh\nzinNJmDdPA0p7egkvmod8ZdWEX95NTQ19zwnE8qRubNxLlyEEwqmMUozFJrUww5CbNcQh+XYFtti\nJ845/hiz/TFm+2KUDmHSraocbFI2HIjT1J74LijPF6aWCB5neD//Gg4TfnU9kVfXET9Y3bPcM6aA\n0JILyFq6mND55+GEbFCrVInHXLZtqGbPzkSPL9m5Aa64dg6z5489aT/oxpzKWVUuYkn22SvuKgdb\nwuxq6KCivoNttYmfUffY93Vpjo+J+UGmFQWZUZSFx1qsh4xGorjbduKu20R83eZEKUgkenSFwnyc\nc2fjXHCe3cx4FmlThz0E2OUG2SdBuuTYVtt8x2WGL8ZUX5wp3sTP3DO8gbI7ud54IE5jMrn2e2B6\n6Znf4JgK8bp6Ims3EFm/AbfXP5/4vATnzyW0YC7B8+YSmDUD8duN12eqpamDjav209yYuIJWPjGf\nRRdNZta8sXitscUMwFmVZFtNdmqNxNotV5X69ihVzV3sa+rq+bm7sZNwzD1mXQFKsn2MzfUzIT/A\nzJIsctM4GuNorsnWeBzdfxB3x+7EtK0Cd+tOiESOriSCjC9Hpk/GmTcHKS8bdOuR1WSnVrqOp6tQ\ng48q/OzXAAcJ0CknlkoUOXHGe13Ge+NM8MYZ541T6nHJET1lq/eRTmVfg8veepeWzqPJdXmBMK5A\n8HqGJqHqqya7P1SV+OEaolu3E92+k/iBAz312wDi8+GfM5PA7BkEZkzFP2MavgnjRnV5SSpqsvui\nqlTtbmTbhmqikUQvUlnZfuZfOIH5iydQMCYr5fscCUbieT2TZURNtohcBXyfxKA4P1fV+/pY54fA\n1UA78G5VPWHkmV27dg11qGeVTZs2DfuHMe4qDR1RDrdGqG2LcLgtQk1rmNq2CDVtEeraoie0TnfL\nC3gozfFTmu1nXL6fKYVBgr6Rc/LZs2NrRifZqgotR3AP1aIHD6P79uNWHcTdtx/ddwC6wie8RspK\nEqUgkycgs6bj5KZm4Jg9B/dZkp1C6TqejkA5UcqJ8hppRxUa8XIIHwfVRw0B6vDR4HpoiHjYGDm2\nFTcoSoknTrHHpcTjUkSc7M4Y0hmjqTnOkY6j3xU+D4wb4uS62+6DeweVZIsI3vKxeMvHElp2OW5b\nO7Fdu4nu3kNsXxVubR3hTVsJb9p69DXBAL6J4xPThPH4Jo7DN64cb1kJTl5uxpdB7KzYNiRJtogw\neUYR4ycXcGBvE3sr6mlt6eKV5yt55flKxhRnM3lmEVNmFjNx6hj8aWygSaV0nNdHs/Xr17Ns2bLT\nrpe2d4+IOMC/A8uAamC1iDyiqtt7rXM1MF1VZ4rIa4D/AE7IVtrb24cp6rNDS0vLoF8bjbt0Rl3a\no3E6InE6oi6d0TjtkTjNnTFauhJT9+Pm5Hx3v9Snku13GBPyMSbLx5iQj7JcH+PyAmT5R05C3Zf2\nttZ0h3AC7QpDWzva1oYeaUs8bm1Dm1rQhka0oRltbEJr6tDDtX0m0j0K8hJJdVkJMn4sztTJSPbQ\ntAZ1dHUOyXbPViPleIpAETGKiDFPEjG5Cs14qcNLreujHi9N6iUWA19U8cTiRCIx2sJRNBqnodf2\noo7QlOWnLcePZnnYL5CDS7brkoUSRAmgBOTo4yAuPhL/AAxWe2dqzkVOTjb+hefhX3gekBi+PVa1\nn9j+A8SrDxE/VIO2tBCpqCRSUXnC6yUYxFtajLekGKcgD09+YnIK8nseewrycfLzcLJCI7JFvK19\naL83vT4PU2YWM3lGEY317ezZUUfdoVYa69tprG9n3T+qEIHComyKx+ZQMjaX4rJc8gqC5OQHycr2\nZ9Q/MmdyXjcn2rBhQ7/WS+e/aEuAClXdByAivwWuB7b3Wud64FcAqvqKiOSLSJmq1hy/sZceWYX2\nur7WnyqY7nUU7T3T97p9vK6vbdGvGLRnvd7r6PGr9LGdo79j3y/U5PqJSXFVcUk8Vk2cuHp+orhu\nYrmixAFcZd2aSv77J08Rd5WY6+K6SsxV4i7E1CXmJlqe464SU8V1E8l1JO7iHlu50cfvfaxQcioH\n/B4h5PUQ8Akhn0PA45Dl85Dt9xDyO3hcgTYSU1IUOPGrQ0/6dzxVLINb9fTbCVdW0/LMmlOvrQpx\nF9x44o/jxsF1k8tc1O39vHvcc8nH8RhEomg0lijXiEbRSDTR73QkCpEI2tkJnV09fVH3OOnJwoGC\nseD3QXYWZGcjeTlIfh6MKUQK85G+uiAbotwtEoXWzjM4saWwOi7zC+0gHIUjHcOXKPT+Djr6XSU9\n8z1va4W4K8RdReNRCuMxcuMwWfuOVYEOv4eWgJf6rACHs4Jo7/d0H1+bfREUP4qPRH/fiQl8KF7p\nY1mv9QTYoz6ed0MIiodE6ZoDOMnnneQkaM/j7nlJri/HxJP8GcqH2fkwe17PMqejA09dLU5tLZ7a\nWjz1DTjNTXhaWqCri2jVAaJVB073J0nw+yAYglAQgkEIBiAUSjwO+MHjBa8XfF7wehKPu5d5k8t8\nvZY5TvKXcZL/tUjip5xk6r1+clnTgcPsWbXh6GsZ4PtUZECvKM6ComkOHZ1Ca7vS2u7SFaYn6d65\n+di0QwSCQQefz8HnFXw+B69X8HgFRwSPA45HcBzBcUj89CSeQ3r9Nt2PBbojll6/rvT8lGP2feJv\nd+rftmpHNS89snoARyQ9HI/w2jctTncYKZPOJHs8sL/X/AESifep1jmYXHbMu/3w4cOsfKVxKGI8\nKx0+UEPzgd4ty0c/8V6coXvTxJNTstE0kpyae57ITLurathR2d/4u1uUBnCUJbm6FxjOLncVGOaP\nXWV1AxXVo+Py7Uiwp7qBXYcy53gKmsjxPEd/BnxKwAeOxEh8ebQT74BOcegUD50IneKhg8R8lzhE\nRYiKQyT5OIJDRISYOIQR+rxu04//qiobG4i4w1TTG8yDiWNh4olP+bs6yWtuJOdIM6H2NrLaW5M/\n2wh1tB2zzB8JI5Fo4j/YI0eGJ/Z+qItWw4tbT7/iKQzmH+Gs5FQGuB4P4fwSusaUEi4spaughFh2\nLtHsfOKBEJ2dLp2dp2xZGjG2bNvHyvKG06+YZhINW5I90kyfPp397X/tmV+wYAELFy5MY0SZbcyM\n61m4sDTdYYwadjxTx45latnxPN6ZXZ9Y71zJwoUj4RpHEBiXnDLT9evXU2rn8ZTJpM/62rVr0x3C\nCdavX39MiUh2dna/Xpe23kVEZCnwZVW9Kjl/N6C9b34Ukf8AnlPV3yXntwOX9VUuYowxxhhjzEiR\nzo4hVwMzRGSyiPiB5cCjx63zKHA79CTlzZZgG2OMMcaYkS5t5SKqGheRjwFPcrQLv20i8sHE0/oz\nVX1cRK4RkV0kuvC7I13xGmOMMcYY01+jYjAaY4wxxhhjRpJRM46oiCwQkX+IyDoRWSUio+f21DQR\nkTtFZJuIbBKRb6Y7nkwnIneJiCsiY9IdSyYTkW8l35frReSPIpKX7pgyjYhcJSLbRWSniHwu3fFk\nMhGZICLPisiW5Hflx9Md02ggIo6IrBWR48tIzQAluz9+MPm9uSU57ogZBBH5lIhsFpGNIvKbZLnz\nSY2aJBv4FvAlVV0EfAn4dprjyWgicjnwZmC+qs4HvpPeiDKbiEwA/gnYl+5YRoEngbmquhCoAP4l\nzfFklF4Dgb0RmAvcIiJz0htVRosBn1bVucBFwEfteKbEJ4Az68PPdPsB8LiqngMsALalOZ6MJCLj\ngDuB81X1PBIl18tP9ZrRlGS7QH7ycQGJPrXN4H0Y+KaqxgBUtT7N8WS67wGfSXcQo4GqPq2q3Z3T\nrgQmpDOeDNQzEJiqRoHugcDMIKjqYVVdn3zcRiKBGZ/eqDJbslHiGuC/0x1Lpkte6Xudqv4SQFVj\nqjpyOkTPPB4gW0S8JLpUrz7VyqMpyf4U8B0RqSLRqm2tW2dmFnCpiKwUkees/GbwROQ6YL+qbkp3\nLKPQe4C/nnYt01tfA4FZUpgCIjIFWAi8kt5IMl53o4TdNHbmpgL1IvLLZPnNz0QklO6gMpGqVgPf\nBapINOQ2q+rTp3pNRg1GIyJPkRiIqWcRiQ/hF4A3AJ9Q1YdF5GbgFyQuz5uTOMXx/FcS741CVV0q\nIhcCvwemDX+UmeE0x/LzHPteHL5xrDPUqT7rqvpYcp0vAFFV/d80hGjMMUQkB/gDifNQW7rjyVQi\nci1Qo6rrk2WL9n15ZrzA+cBHVXWNiHwfuJtEWa0ZABEpIHHVbzLQAvxBRG491Tkoo5JsVT1p0iwi\nv1bVTyTX+4OI/Hz4IstMpzmeHwIeSq63OnnDXpGqjvxxWdPgZMdSROYBU4ANIiIkShteFZElqlo7\njCFmlFO9NwFE5N0kLie/flgCGl0OApN6zU/AyuvOSPLS8R+AX6vqI+mOJ8NdDFwnItcAISBXRH6l\nqrenOa5MdYDEldQ1yfk/AHaz8+C8AahU1UYAEXkIeC1w0iR7NJWLHBSRywBEZBmwM83xZLqHSSYw\nIjIL8FmCPXCqullVx6rqNFWdSuILb5El2IMnIleRuJR8naqG0x1PBurPQGBmYH4BbFXVH6Q7kEyn\nqp9X1UmqOo3Ee/NZS7AHLzmA3/7keRxgGXZD6WBVAUtFJJhsNFvGaW4izaiW7NN4P/BDEfEAXcAH\n0hxPpvsl8AsR2QSESY68ac6YYpc/z9SPAD/wVOJ7jpWq+pH0hpQ5TjYQWJrDylgicjFwG7BJRNaR\n+Ix/XlWfSG9kxvT4OPAbEfEBldjAfoOiqqtE5A/AOiCa/PmzU73GBqMxxhhjjDEmxUZTuYgxxhhj\njDEjgiXZxhhjjDHGpJgl2cYYY4wxxqSYJdnGGGOMMcakmCXZxhhjjDHGpJgl2cYYY4wxxqSYJdnG\nGGOMMcakmCXZxhhjjDHGpJgl2cYYY4wxxqSYJdnGGGOMMcakmCXZxhhjjDHGpJg33QEYY4wZXiJy\nHRAHXgdsAq4C7lXVHWkNzBhjRhFR1XTHYIwxZpiIyCTAr6q7RORVYBlwMfCsqnamNzpjjBk9rCXb\nGGPOIqpaBSAipcARVW0G/pLeqIwxZvSxmmxjjDmLiMgcEVkAXAO8mFz2pvRGZYwxo4+1ZBtjzNnl\nSiAHOAQEReQG4GB6QzLGmNHHarKNMcYYY4xJMSsXMcYYY4wxJsUsyTbGGGOMMSbFLMk2xhhjjDEm\nxSzJNsYYY4wxJsUsyTbGGGOMMSbFLMk2xhhjjDEmxSzJNsYYY4wxJsUsyTbGGGOMMSbF/j9W6iOk\nYEPKHgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d79f7ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "\n",
    "nor = stats.norm\n",
    "x = np.linspace(-8, 7, 150)\n",
    "mu = (-2, 0, 3)\n",
    "tau = (.7, 1, 2.8)\n",
    "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\"]\n",
    "parameters = zip(mu, tau, colors)\n",
    "\n",
    "for _mu, _tau, _color in parameters:\n",
    "    plt.plot(x, nor.pdf(x, _mu, scale=1. / np.sqrt(_tau)),\n",
    "             label=\"$\\mu = %d,\\;\\\\tau = %.1f$\" % (_mu, _tau), color=_color)\n",
    "    plt.fill_between(x, nor.pdf(x, _mu, scale=1. / np.sqrt(_tau)), color=_color,\n",
    "                     alpha=.33)\n",
    "\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.xlabel(\"$x$\")\n",
    "plt.ylabel(\"density function at $x$\")\n",
    "plt.title(\"Probability distribution of three different Normal random \\\n",
    "variables\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n",
    "\n",
    "$$ E[ X | \\mu, \\tau] = \\mu$$\n",
    "\n",
    "and its variance is equal to the inverse of $\\tau$:\n",
    "\n",
    "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n",
    "\n",
    "\n",
    "\n",
    "Below we continue our modeling of the Challenger space craft:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pymc as pm\n",
    "\n",
    "temperature = challenger_data[:, 0]\n",
    "D = challenger_data[:, 1]  # defect or not?\n",
    "\n",
    "# notice the`value` here. We explain why below.\n",
    "beta = pm.Normal(\"beta\", 0, 0.001, value=0)\n",
    "alpha = pm.Normal(\"alpha\", 0, 0.001, value=0)\n",
    "\n",
    "\n",
    "@pm.deterministic\n",
    "def p(t=temperature, alpha=alpha, beta=beta):\n",
    "    return 1.0 / (1. + np.exp(beta * t + alpha))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n",
    "\n",
    "$$ \\text{Defect Incident, $D_i$} \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n",
    "\n",
    "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the above code we had to set the values of `beta` and `alpha` to 0. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `pm.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in PyMC. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,\n",
       "        0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,\n",
       "        0.5])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 120000 of 120000 complete in 9.6 sec"
     ]
    }
   ],
   "source": [
    "# connect the probabilities in `p` with our observations through a\n",
    "# Bernoulli random variable.\n",
    "observed = pm.Bernoulli(\"bernoulli_obs\", p, value=D, observed=True)\n",
    "\n",
    "model = pm.Model([observed, beta, alpha])\n",
    "\n",
    "# Mysterious code to be explained in Chapter 3\n",
    "map_ = pm.MAP(model)\n",
    "map_.fit()\n",
    "mcmc = pm.MCMC(model)\n",
    "mcmc.sample(120000, 100000, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lIxzKRfkIZqIuIiIiIiK7BTNR1zrq4dD6q2HROuphUT7CofeqsCgf4VAuyodq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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d7a3f278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha_samples = mcmc.trace('alpha')[:, None]  # best to make them 1d\n",
    "beta_samples = mcmc.trace('beta')[:, None]\n",
    "\n",
    "figsize(12.5, 6)\n",
    "\n",
    "# histogram of the samples:\n",
    "plt.subplot(211)\n",
    "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n",
    "plt.hist(beta_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
    "         label=r\"posterior of $\\beta$\", color=\"#7A68A6\", normed=True)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.hist(alpha_samples, histtype='stepfilled', bins=35, alpha=0.85,\n",
    "         label=r\"posterior of $\\alpha$\", color=\"#A60628\", normed=True)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n",
    "\n",
    "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n",
    "\n",
    "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected).  \n",
    "\n",
    "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "t = np.linspace(temperature.min() - 5, temperature.max() + 5, 50)[:, None]\n",
    "p_t = logistic(t.T, beta_samples, alpha_samples)\n",
    "\n",
    "mean_prob_t = p_t.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Vhxtp9/rhcGOX+ROn5eGJ0DH/9l+2s23nQVI9B0hJi+989NTAV/3XUz57TEoS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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d73278d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 4)\n",
    "\n",
    "plt.plot(t, mean_prob_t, lw=3, label=\"average posterior \\nprobability \\\n",
    "of defect\")\n",
    "plt.plot(t, p_t[0, :], ls=\"--\", label=\"realization from posterior\")\n",
    "plt.plot(t, p_t[-2, :], ls=\"--\", label=\"realization from posterior\")\n",
    "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n",
    "plt.title(\"Posterior expected value of probability of defect; \\\n",
    "plus realizations\")\n",
    "plt.legend(loc=\"lower left\")\n",
    "plt.ylim(-0.1, 1.1)\n",
    "plt.xlim(t.min(), t.max())\n",
    "plt.ylabel(\"probability\")\n",
    "plt.xlabel(\"temperature\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n",
    "\n",
    "\n",
    "An interesting question to ask is for what temperatures are we most uncertain about the defect-probability? Below we plot the expected value line **and** the associated 95% intervals for each temperature. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ez371g/z83m/w8utP0elrT3RofRrNuU52DqdFa4uPLX/bRW11K6A1qHbTfNtL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d6d7cba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats.mstats import mquantiles\n",
    "\n",
    "# vectorized bottom and top 2.5% quantiles for \"confidence interval\"\n",
    "qs = mquantiles(p_t, [0.025, 0.975], axis=0)\n",
    "plt.fill_between(t[:, 0], *qs, alpha=0.7,\n",
    "                 color=\"#7A68A6\")\n",
    "\n",
    "plt.plot(t[:, 0], qs[0], label=\"95% CI\", color=\"#7A68A6\", alpha=0.7)\n",
    "\n",
    "plt.plot(t, mean_prob_t, lw=1, ls=\"--\", color=\"k\",\n",
    "         label=\"average posterior \\nprobability of defect\")\n",
    "\n",
    "plt.xlim(t.min(), t.max())\n",
    "plt.ylim(-0.02, 1.02)\n",
    "plt.legend(loc=\"lower left\")\n",
    "plt.scatter(temperature, D, color=\"k\", s=50, alpha=0.5)\n",
    "plt.xlabel(\"temp, $t$\")\n",
    "\n",
    "plt.ylabel(\"probability estimate\")\n",
    "plt.title(\"Posterior probability estimates given temp. $t$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *95% credible interval*, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n",
    "\n",
    "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over [0,1] quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What about the day of the Challenger disaster?\n",
    "\n",
    "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring,  given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VMpmvfNSTWSMzZszodBdsEHG8WF6OFSvC8WKdVMpk3szMzMzMmitlMt/7sH2zZg466KBO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\nBikn82ZmZmZmg5STeTMzMzOzQer/A1dJ6Q5qeTrJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d7ac1da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 2.5)\n",
    "\n",
    "prob_31 = logistic(31, beta_samples, alpha_samples)\n",
    "\n",
    "plt.xlim(0.995, 1)\n",
    "plt.hist(prob_31, bins=1000, normed=True, histtype='stepfilled')\n",
    "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n",
    "plt.xlabel(\"probability of defect occurring in O-ring\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Is our model appropriate?\n",
    "\n",
    "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n",
    "\n",
    "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data (which if we recall is a *fixed* stochastic variable) with an artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n",
    "\n",
    "Previously in this Chapter, we simulated artificial datasets for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example,  we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to create a new `Stochastic` variable, that is exactly the same as our variable that stored the observations, but minus the observations themselves. If you recall, our `Stochastic` variable that stored our observed data was:\n",
    "\n",
    "    observed = pm.Bernoulli( \"bernoulli_obs\", p, value=D, observed=True)\n",
    "\n",
    "Hence we create:\n",
    "    \n",
    "    simulated_data = pm.Bernoulli(\"simulation_data\", p)\n",
    "\n",
    "Let's simulate 10 000:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 10000 of 10000 complete in 1.5 sec"
     ]
    }
   ],
   "source": [
    "simulated = pm.Bernoulli(\"bernoulli_sim\", p)\n",
    "N = 10000\n",
    "\n",
    "mcmc = pm.MCMC([simulated, alpha, beta, observed])\n",
    "mcmc.sample(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 23)\n"
     ]
    },
    {
     "data": {
      "image/png": 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NpKdlvDVnn5eyPwJzgEHgWnf/fn59mkc9HK2tmn81JMojLMojHMoiLMojHMoi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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d736f1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(12.5, 5)\n",
    "\n",
    "simulations = mcmc.trace(\"bernoulli_sim\")[:]\n",
    "print(simulations.shape)\n",
    "\n",
    "plt.title(\"Simulated dataset using posterior parameters\")\n",
    "figsize(12.5, 6)\n",
    "for i in range(4):\n",
    "    ax = plt.subplot(4, 1, i + 1)\n",
    "    plt.scatter(temperature, simulations[1000 * i, :], color=\"k\",\n",
    "                s=50, alpha=0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n",
    "\n",
    "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n",
    "\n",
    "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [7] than p-value tests. We agree.\n",
    "\n",
    "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[8]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n",
    "\n",
    "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "posterior prob of defect | realized defect \n",
      "0.41                     |   0\n",
      "0.24                     |   1\n",
      "0.28                     |   0\n",
      "0.32                     |   0\n",
      "0.36                     |   0\n",
      "0.18                     |   0\n",
      "0.16                     |   0\n",
      "0.25                     |   0\n",
      "0.77                     |   1\n",
      "0.54                     |   1\n",
      "0.24                     |   1\n",
      "0.07                     |   0\n",
      "0.37                     |   0\n",
      "0.86                     |   1\n",
      "0.36                     |   0\n",
      "0.11                     |   0\n",
      "0.24                     |   0\n",
      "0.05                     |   0\n",
      "0.10                     |   0\n",
      "0.06                     |   0\n",
      "0.12                     |   1\n",
      "0.10                     |   0\n",
      "0.75                     |   1\n"
     ]
    }
   ],
   "source": [
    "posterior_probability = simulations.mean(axis=0)\n",
    "print(\"posterior prob of defect | realized defect \")\n",
    "for i in range(len(D)):\n",
    "    print(\"%.2f                     |   %d\" % (posterior_probability[i], D[i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we sort each column by the posterior probabilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "probb | defect \n",
      "0.05  |   0\n",
      "0.06  |   0\n",
      "0.07  |   0\n",
      "0.10  |   0\n",
      "0.10  |   0\n",
      "0.11  |   0\n",
      "0.12  |   1\n",
      "0.16  |   0\n",
      "0.18  |   0\n",
      "0.24  |   1\n",
      "0.24  |   1\n",
      "0.24  |   0\n",
      "0.25  |   0\n",
      "0.28  |   0\n",
      "0.32  |   0\n",
      "0.36  |   0\n",
      "0.36  |   0\n",
      "0.37  |   0\n",
      "0.41  |   0\n",
      "0.54  |   1\n",
      "0.75  |   1\n",
      "0.77  |   1\n",
      "0.86  |   1\n"
     ]
    }
   ],
   "source": [
    "ix = np.argsort(posterior_probability)\n",
    "print(\"probb | defect \")\n",
    "for i in range(len(D)):\n",
    "    print(\"%.2f  |   %d\" % (posterior_probability[ix[i]], D[ix[i]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can present the above data better in a figure: I've wrapped this up into a `separation_plot` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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B8L/PWxdVD2ujamFtrFtk5pEbRKwEPpGZa9rxtUB2L6SOiM8D38nMu9rxLuD3e6cwXXbZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d7995dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from separation_plot import separation_plot\n",
    "\n",
    "\n",
    "figsize(11., 1.5)\n",
    "separation_plot(posterior_probability, D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects.  As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n",
    "\n",
    "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n",
    "\n",
    "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n",
    "\n",
    "1. the perfect model, which predicts the posterior probability to be equal to 1 if a defect did occur.\n",
    "2. a completely random model, which predicts random probabilities regardless of temperature.\n",
    "3. a constant model:  where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23.  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d799c198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d799c208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d6d39b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d74f3b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize(11., 1.25)\n",
    "\n",
    "# Our temperature-dependent model\n",
    "separation_plot(posterior_probability, D)\n",
    "plt.title(\"Temperature-dependent model\")\n",
    "\n",
    "# Perfect model\n",
    "# i.e. the probability of defect is equal to if a defect occurred or not.\n",
    "p = D\n",
    "separation_plot(p, D)\n",
    "plt.title(\"Perfect model\")\n",
    "\n",
    "# random predictions\n",
    "p = np.random.rand(23)\n",
    "separation_plot(p, D)\n",
    "plt.title(\"Random model\")\n",
    "\n",
    "# constant model\n",
    "constant_prob = 7. / 23 * np.ones(23)\n",
    "separation_plot(constant_prob, D)\n",
    "plt.title(\"Constant-prediction model\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n",
    "\n",
    "The perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Exercises\n",
    "\n",
    "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples.  Why might the resulting plot look like this?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6565Qq5aTy8H4uFYXtLIAPpWyxa0SCRgYgO7ugJaWiELBFqiKooj+fiWbhe5u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\nMcYYY0yVs6TeGGOMMcaYKvf/A9xHQXd0r+z6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f80d794c438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# type your code here.\n",
    "figsize(12.5, 4)\n",
    "\n",
    "plt.scatter(alpha_samples, beta_samples, alpha=0.1)\n",
    "plt.title(\"Why does the plot look like this?\")\n",
    "plt.xlabel(r\"$\\alpha$\")\n",
    "plt.ylabel(r\"$\\beta$\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References\n",
    "\n",
    "-  [1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n",
    "-  [2] German Rodriguez. Datasets. In WWS509. Retrieved 30/01/2013, from <http://data.princeton.edu/wws509/datasets/#smoking>.\n",
    "-  [3] McLeish, Don, and Cyntha Struthers. STATISTICS 450/850 Estimation and Hypothesis Testing. Winter 2012. Waterloo, Ontario: 2012. Print.\n",
    "-  [4] Fonnesbeck, Christopher. \"Building Models.\" PyMC-Devs. N.p., n.d. Web. 26 Feb 2013. <http://pymc-devs.github.com/pymc/modelbuilding.html>.\n",
    "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. <https://plus.google.com/u/0/107971134877020469960/posts/KpeRdJKR6Z1>.\n",
    "- [6] S.P. Brooks, E.A. Catchpole, and B.J.T. Morgan. Bayesian animal survival estimation. Statistical Science, 15: 357–376, 2000\n",
    "- [7] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n",
    "- [8] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from IPython.core.display import HTML\n",
    "\n",
    "\n",
    "def css_styling():\n",
    "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda env:bayes]",
   "language": "python",
   "name": "conda-env-bayes-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
